You will get these naturally by progressing through a playthrough, as long as you don't have a mutiny or lose all your crew. Don't worry if some of these achievements don't unlock at the exact point I've mentioned, sometimes they will unlock a bit later, or together at the end of the playthrough. I personally had the achievements for Acts 3, 4, and 5 all unlock at once at the end of my first run.

Some of the week numbers may be slightly off (since I unlocked these achievements at the end of my run and not during the actual story event) so if you can suggest a more accurate number, kindly inform me in the comments.

Prologue
Story-related, unmissable.
Unlocked after the first vote in Week 4.

Act I
Story-related, unmissable.
Unlocked after the encounter with the leopard seal, in Week 12 (approx).

Act II
Story-related, unmissable.
Unlocked after meeting the penguin colony, in Week 16 (approx).

Act III
Story-related, unmissable.
Unlocked after surviving the winter, in Week 36 (approx).

Act IV
Story-related, unmissable.
Unlocked after climbing the mountain, in Week 39 (approx).

Act V
Story-related, unmissable.
Unlocked after the second vote, in Week 40-42.

This section is for loyalty-related achievements for each of the specialist/leader characters.

My general advice is to just be nice to all the different characters, tell them they are valuable, their hard work is appreciated, and choose dialog options that suit their personalities. Obviously you also gain loyalty by agreeing to and fulfilling a character's request (or their followers' requests, if they have any). You will also get -20 loyalty penalty from a leader if their follower dies.

In general, I found Kurt, Kasha, Dr Arthur, and Templeton were the easiest to attain loyalty from because all of them already start loyal, and you will have many opportunities to boost loyalty with each of them. They also have fairly low thresholds, except Templeton. Therefore it's okay to sometimes sacrifice loyalty from these characters if you can gain loyalty from Grimley, Junior, Cordell, or Hammond in return.

It seems Grimley is the hardest to attain loyalty from since he starts with the least, and also has the highest threshold. Therefore I have included a (non-exhaustive) list of interactions that have large loyalty changes with Grimley, and a few smaller ones.

If you would like me to include more such events for Grimley and/or for other characters, or if you wish to suggest more events I haven't recorded - please leave a comment, so I can add to the guide and give you credit.

The Carpenter
Survive with Grimley alive and loyal to you.

- very loyal to Hunt
- does NOT like you talking poorly of Hunt or doubting his captaincy
- does NOT like you asserting yourself as Captain
- does not like sarcastic comments
Loyalty events:
-5 for giving Stanberry the Captain's hat and letting her destroy it
-5 for telling him it "wouldn't be a complete loss" if he stopped playing in Week 5
-5 for saying you think the rumours about Captain Hunt's ghost are harmless in Week 6
-15 for sarcastically saying you will "watch out for Captain Hunt's ghost" in Week 6
-5 for saying you are the new Captain and will "steer them right" after dinner in Week 6
-5 for insisting that you are the new Captain and don't care about the vote after dinner in Week 6
-50 for smashing his accordion
-5 for telling Runt he should stay with his father during winter when he wants to move tents (no loyalty loss if you tell him it's not possible/there's no space)
+5 for asking how to get on good terms with the crew
+5 for making the scientists watch the radios in Week 5
+5 for telling him to keep playing for the crew's sake, or suggesting playing close to the furnace in Week 5
+5 for saying Hunt was a good Captain after dinner in Week 6
+10 for stopping the rumours about Captain Hunt's ghost in Week 6
+10 for stepping in between Kurt and Hammond when they are arguing about locking down for winter, and separating them physically by yourself
+10 for telling Runt he should grow into a sailor when he wants to do something else and retrain
+5 for letting Runt move to a different tent during winter
+5 for giving Hunt's Captain Hat to either him or Junior in Week 37, when you are leaving the ice on lifeboats
+5 for celebrating when you find the Viscount in the mountain cave, and swearing like a sailor
(credit to users @criminalscum, @OkayCadet, @SteemPoweredSweetheart, @riptrees for the following additions):
+10 for sparing timber for making totems in Week 16 (requires you to have at least 1 timber left from the ship)
+20 for telling Templeton to back off when Grimley is playing music mocking you for the 2nd time
+5 for telling Grimley that you miss the rocking of the boat in Week 7
-10 for omitting to mention Hunt and his deserting sailors during the eulogy in Act 4

The Cook
Survive with Junior alive and loyal to you.

- appreciates compliments to his cooking
- appreciates honesty and clarity, dislikes lying
- likes being told he is valuable to the crew

The Doctor
Survive with Dr Arthur Nutlee alive and loyal to you.

- reacts well to encouragement and reassurance
- reacts poorly to doubting his abilities as a doctor
- likes being reminded he is saving lives and is valuable to the crew

The Engineer
Survive with Hammond alive and loyal to you.

- dislikes being told to rest or take a break, he prefers working
- likes being told he is valuable and doing a good job
- dislikes Templeton
- does not want any leadership role, he just wants to work and mind his own business
- likes sarcastic humour

The Journalist
Survive with Kasha alive and loyal to you.

- appreciates friendly greetings and talk of civilian life, as she is a civilian
- is loyal to journalistic integrity, does NOT like being told what to put in her report
- does not like sailing or being reminded you have a long trip, she is not a sailor

The Kennelmaster
Survive with Cordell alive and loyal to you.

- likes it when you interact positively with her dogs
- reacts well to you discussing music and encouraging her to hang out with the crew
- is very apologetic if she shoots you; gains a lot of respect for you if you choose not to shoot her during the duel

The Navigator
Survive with Kurt alive and loyal to you.

- likes honesty and encouragement when he is doubting himself
- wants to protect his image, dislikes being embarrassed publicly and dislikes the idea of Kasha's report hurting his reputation

The Science Officer
Survive with Templeton alive and loyal to you.

- very focused and driven, and dedicated to the mission of finding the Viscount
- appreciates you following his advice
- likes it when rules and "proper procedure" are followed and the crew is obedient
- likes discussing science and academic topics

Bonded
Survive the ice with all crew alive and loyal.

Just follow the advice for each character above and end your playthrough with all characters (including followers, not just specialist leaders) alive and loyal to your captaincy. This will also ensure you get the "good" endings, whichever way you go. This should also unlock "An Ernest Attempt" by default, please check the steps for that achievement below too. Also compatible with the achievements "Captain Shaw", "Envoyage", "Dispersal", and "Beneficial", depending on your previous choices.

Immutable Mutiny
Have no loyalty left from anyone.

Just get everyone disloyal and do the opposite of the advice for the previous achievements. You don't need to get everyone down to exactly 0 loyalty like the description implies, it's enough if they are just below the loyalty threshold. You can also kill off a character after they are disloyal, you don't need to keep them all alive either. Compatible with the achievements "Old Reliable", "Middle Management", "Deplorable", and "Comeuppance", depending on your previous choices and which characters are still alive by the end.

These achievements are obtained at specific times or through specific choices/tasks during a playthrough. Organized in (approximate) chronological order within a playthrough.

Internship
Bring the Stowaway there and back again.

Your crew will find a young boy nicknamed "Runt" in the Prologue. Let him stay and keep him alive for the entire playthrough. Since the achievement says "and back again", I assume you also need to win the vote, either at the Viscount or with Appertton, so that you can actually bring him back, but not 100% sure. I got this after winning the vote to become Captain and sailing back with the Viscount.

Short Staffed
Survive the ice without bringing Runt and their father.

Refuse to let Runt stay and also choose to dismiss his father from the expedition, and finish a playthrough.

First Encounters
Meet all crew members in the prologue.

Just be judicious about checking for conversation or interactable icons before advancing the story for the first 4 weeks. The easiest crew to miss are the scientists and the scouts:

• You can find 2 scientists in the corners of the middle deck in the first 2 weeks, just zoom out so you don't miss them;
  
• During Week 3, you can find a locked door next to your cabin. You must knock 3 or 4 times to meet the scientist Isaac;
  
• You can meet 1 scout on the rigging in Week 3, next to the Crow's Nest;
  
• The remaining 2 scouts will be in the room next to the Doctor's Infirmary.

Isaac's Gun
Let the scientist keep his weapon.

When taking requests in Week 6, you will meet the scientist Isaac and Templeton will inform you that he has a gun. Let him keep his revolver for the achievement.
I've heard the unlock trigger for this achievement is inconsistent so if it doesn't trigger immediately, just continue with your playthrough and it may unlock at the end of the playthrough like Kasha's camera. It can possibly also unlock if you choose to fire a gun during Kurt and Hammond's argument in Week 16; if you let Isaac keep the revolver, he will fire it instead and the achievement should unlock.
(thank you to @Evan the Illiterate, Phd for confirming)

Down with the Ship
Go down with the Temperance.

Fail to evacuate the Temperance by Week 8 and sink below the ice. This will also end your current run.

The Ice Doesn't Care You're Here
Get your first crew member killed.

Outside of starving and freezing your crew to death, there are several story events for this:

• End of Act 1 with the leopard seal. Fail to kill the leopard seal and it will kill Kurt's scout.
  
• Act 3, Dr Arthur will try to leave during the winter. You can antagonize him and tell him he's useless, he will leave the following week and die in the storm. Do NOT say his father would be ashamed if you want to kill him, because then he will stay just to spite you.
  
• Act 4, when you are boarding crew onto the lifeboats, to sail over the ocean. You command Lifeboat 1, Junior and Grimley command Lifeboats 2 and 3. The more sick, wounded, freezing, and starving crew you load onto their lifeboats, the more likely their boats are to sink.
  
• Act 4, when Cordell tries to escape over the mountain with Stanberry. Hammond will wake you and you can chase her up the mountain. Draw your gun and fire to immediately kill her. You can also kill Hammond after asking him to hide the body.
  
• End of Act 4 at the mountain, when Kasha drops her camera. After Kurt and Kasha recover the camera they will start climbing up, you can cut the rope to kill them both.

The Importance of Maintaining Decorum
Succumb to the ice.

Go below 0 decorum and end the week, causing your crew to mutiny. Sometimes you have to go an additional week at 0 decorum to get the mutiny event to trigger. Also make sure that the "Disable Decorum Game Overs" option in the settings is unchecked.

Sound Decision
Smash the carpenter's accordion.

Templeton will inform you on Week 12 or 13 that Grimley is playing mutiny-encouraging songs that mock your leadership. After you eat dinner you will hear the song yourself. Simply smash Grimley's accordion for the achievement.

Within Earshot
Lose an ear.

Follow Cordell up the mountain in Act 4, Week 38 when Hammond wakes you and tells you she has run away. Challenge her to a duel and then purposely don't shoot; she will shoot first and take off your ear. You also get a huge loyalty bonus.
(credit to @Evan the Illiterate, Phd for discovery)

A Thousand Words
Kasha's camera survives the expedition.

Let Kurt and Kasha save Kasha's camera at the end of Act 4, Week 38-39, when it falls off a cliff. Achievement should unlock at the end of the playthrough. You can save both Kurt and Kasha by encouraging Kurt to save Kasha when the rope starts tearing, or threatening to cut Kasha's rope yourself if he thinks about sacrificing himself. If you're really cruel, you can still get the camera by starting to cut the rope and telling them to give you the camera, then cutting the rope anyway and killing both of them.

...For Warmth
Find love on the ice.

If Dr Arthur, Kasha, and Kurt are all alive by the end of Act 4, you will find Kasha and Dr Arthur kissing behind a tent after you reach the top of the mountain. Kurt must survive the camera rescue event at the cliff, so that your crew isn't depressed from his death and you can observe this event. You can gain loyalty bonuses with both by encouraging their relationship. Achievement should unlock at the end of the conversation.
(credit to @SteemPoweredSweetheart for discovering that Kurt's survival matters)

These achievements are mostly related to the Viscount ending (enter the mountain cave in Act 5 and find the Viscount). Some achievements are not only exclusively obtained in this ending, but are easiest obtained this way.

Please note that these achievements will unlock at the end of a playthrough, after you complete the epilogue (final cutscene where you write in your journal).

A Commitment Kept
Forgo rescue to complete the mission.

Don't look for rescue outside the mountain cave on Week 39. Enter the cave and find the Viscount. I got this by sailing it back, I'm not sure if you can get this if you burn it instead.

A Fruitless Endeavour
Survive the ice, unstained.

Enter the mountain cave to find the Viscount, but don't eat the fruit when Hunt offers it to you. I recommend doing this before eating the fruit, otherwise you may need a brand new run for this achievement.

Awareness
Become stained with awareness.

Eat the fruit when Hunt offers it to you. This allows you to access previously "locked" weeks and branch out in more directions. It also allows you to convince Hunt of an "alternative path", which is necessary for "Worth his Salt" (see description in next section below).

Captain Shaw
Win the vote at the Viscount and survive.

Win the vote at the Viscount (not the vote on Week 4) to officially become Captain. You must have the loyalty of at least half the surviving crew for this - visit the Loyalty section of the guide for how to manage this.

Terminus
Convince Hunt to sail home with you on the Viscount.

Be nice to Hunt when you find him on the Viscount, don't be rude or insult him. I'm not sure what are the exact trigger conditions but this is what I did:
- All crew alive and loyal;
- Tell Hunt all about your journey, e.g. Kasha dropped her camera, Cordell tried to escape, etc.;
- Tell Hunt you need to consult the crew about the tree at the end of the conversation. Hunt will reply that he is "still making up his mind";
- Take Hunt along as a free man;
- Do NOT burn the Tree. I recommend taking samples;
- Hunt will insist on burning the Tree, promise him that Apertton won't get their hands on it;
- Sail home on the Viscount (also unlocks "Dispersal").
(thank you to @Evan the Illiterate, Phd for confirming)
(credit to @SteemPoweredSweetheart for discovering all crew must be alive+loyal)

Dispersal
Sail the Viscount home.

Find the Viscount in the mountain cave, win the vote, and do not burn the Tree so you can sail it back.

Envoyage
Send out an envoy for rescue.

Find the Viscount in the mountain cave and win the vote. When choosing the fate of the Viscount Tree, you can either sail it back, burn it, or send an envoy to come rescue you. Choose to send an envoy to come rescue you.

Up in Flames
Observe the Viscount burn.

Find the Viscount in the mountain cave. Don't eat the fruit when Hunt offers it to you, and insist on burning the Tree when you bring him back to the rest of the crew. This decision will drop some of Templeton's loyalty, so ensure you have enough loyalty to win the following vote. Choose to burn the Tree and the Viscount, and send an envoy to sail home safely. Hunt's fate doesn't matter.

An Ernest Attempt
Survive the ice with all crew alive.

Make sure nobody dies or abandons your crew. Loyalty doesn't matter for this achievement. This goes for the specialists/leaders, AND the individual crew, you must have a fully intact crew by the time you reach the Viscount. Achievement will unlock at the end of the playthrough. You should also get this by default if you get "Bonded".
There are a few things that can make this difficult for you:
- Manage your rations well and ensure nobody has their symptoms worsen from frostbite or scurvy. You can alternate low rations/normal rations each week to save on resources and make sure nobody gets too sick.
- You must protect Kurt's scout from the leopard seal at the end of Act 1. I recommend using the Bolt-Action Rifle; Revolver doesn't do enough damage and Shotgun takes too long to reload. Shoot the seal as soon as you see it, reload once, and the 2nd shot should kill it.
- Dr Arthur Nutlee will try to leave in Act 3 (approx Week 30) during the winter. Keep his loyalty high by encouraging him; reassure him that he is valuable to the crew so he doesn't leave and die.
- Cordell will try to leave in Act 4, Week 38. Hammond will wake you up and tell you Cordell is missing. Follow him and sneak up the mountain. Just be nice, don't draw your gun, and tell her that Hammond needs another level-headed person, which convinces her to stay with your crew. Alternatively, you can challenge her to a duel and refuse to shoot. She shoots you instead ("Within Earshot" ). You also get a +20 loyalty bonus and if she is loyal by now, she will return to camp.
- Kasha's camera falls off a cliff in Act 4, Week 38-39. Kurt will volunteer to help. While recovering the camera, the rope will start tearing and Kurt will try to sacrifice himself. Encourage him to save Kasha (or threaten him that you will cut Kasha's rope) so that both survive.

Old Reliable
Survive the ice with Hunt as Captain.

Lose the vote at the Viscount and have Hunt retain his Captaincy. Junior and Grimley are loyal to Hunt when disloyal to you. Just keep them disloyal, which will give Hunt +10 votes. For everybody else, either make them disloyal or kill them off, doesn't matter. Just ensure you have less than +10 votes favouring you by Week 39.

Down in Flames
Seal your own fate.

Have Hunt win the Viscount vote, and attack him when he tries to burn the tree. You will get overpowered and he will leave you to burn with the Viscount. Alternatively, you can also burn the tree if Templeton wins the vote ("Middle Management").
(credit to @Evan the Illiterate, Phd and @ChelsElixir for discovery)

Middle Management
Survive the ice with Templeton as Captain.

This is a tricky one. First, I recommend checking the steps for "Deplorable" in the next section below. I used the same strategy as "Deplorable", except:
- I kept Dr Arthur loyal and alive - not strictly necessary, but it helps to have him alive;
- I kept only the scientists healthy during winter (heal the scientists with medical comforts, then have the scientists make more comforts). Everybody else was starving, frostbitten, etc.
- I put the scientists on Lifeboat 1, so they survived while everybody else drowned on Lifeboats 2+3;
- disloyal Templeton;
- find the Viscount in the mountain cave.
By this point, only the scientists and Dr Arthur should be alive, everybody else is dead. Since Templeton is disloyal, he will run for Captain, the 3 scientists vote for him. Dr Arthur is outvoted, everybody else is dead so they abstain by default, so Templeton becomes Captain.

These achievements are mostly related to the Appertton ending (ignore the mountain cave in Act 5 and seek rescue). Some achievements are not only exclusively obtained in the Appertton ending, but are easiest obtained this way.

Please keep in mind that these achievements will unlock at the end of a playthrough, after you complete the epilogue and the final cutscene where you write in your journal for the last time.

A Quest Abandoned
Abandon the mission to seek rescue.

At the top of the mountain, in Act V - Week 39, Templeton will ask you to continue the mission and search inside the mountain cave. Tell him whatever you want to end the conversation. Ignore the mountain cave and look to the shore instead to seek rescue. Compatible with achievements "Beneficial", "Detained", "Deplorable", and "Comeuppance" detailed below.

Beneficial
Survive the ice with Minerva's support.

You need to convince Minerva Appertton that you are a proficient Captain and did the best you could.

• Abandon the quest to find the Viscount in Act 5, seek rescue instead;
  
• Make sure your crew is loyal (especially Templeton, he is very important for this ending);
  
• Follow the story to eventually meet Minerva Appertton on the rescue ship;
  
• Tell her that you prioritized your crew over her mission, and that it's ridiculous that she wants to arrest you;
  
• If Templeton is loyal, he will vouch for you. Appertton will ask the rest of the crew to vote, and also check your research;
  
• If the majority of the crew votes in your favour, she will decide not to arrest you after all;
  
• Every 10 points of research you've collected will also add +1 vote in your favour. So, for example, 26 research is considered as +20 research which gives you +2 votes.

Win this vote and sail home as a free man.

Detained
Survive the ice as Minerva's prisoner.

Same as above, but fail to convince Minerva that you are a proficient Captain. It seems there are a few hidden conditions:

• Tell her you intentionally abandoned the mission;
  
• Templeton is disloyal;
  
• You have less than 10 research;
  
• At least some of your crew must be alive and loyal;
  
• Most of your crew is disloyal, but not all (otherwise you get marooned).

I got this by having Junior, Grimley, and Dr Arthur loyal, while Cordell, Kasha, Kurt, and Hammond were all disloyal and dead (so their followers abstained). Templeton was alive and disloyal so he abstained too. The final tally was +11 (in favour), -13 (abstained), so Appertton was unconvinced and had me arrested for breaching contract. Since Templeton was disloyal and Kasha fell off the cliff with her camera, research wasn't counted either.

Worth his Salt
Offer Hunt an alternative and see it through.

So this one requires a bit of rewinding. Also be sure to find a save point where all of your crew is alive and loyal.

1. First you have to eat the fruit Hunt offers you, and gain awareness. Complete this playthrough however you like and press "Continue" on the main menu to access your save tree again;
   
2. Most of your save tree will now turn purple due to gaining awareness. Previously your furthest save point would be right when you find the Viscount, but now you should have a new save point above that, which shows a conversation with Hunt. Remember this, we will be returning to this save point later;
   
3. Rewind to the week before (make sure you are rewinding on a purple savetree, in case you have multiple save files), and this time choose to not find the Viscount but search for rescue instead. Say whatever you want to Appertton and reach the ending again. This will ensure your character now has "awareness" of the Appertton ending, and this branch should also be purple on your savetree;
   
4. Now, return to that "new" save point we discovered earlier in Step 2, that has the conversation with Hunt. You should now see a "fruit" icon next to one of the dialog options and you can tell him that Appertton is arriving with her ship. Finish the story, however you like.
   
5. Rewind again to the week before, and once again abandon the Viscount mission and search for rescue.
   
6. When you meet Appertton this time, she will ask what happened to Hunt. You will now have a new option with the fruit icon again, "Hunt went down with the ship". Select this option and win the vote to unlock the achievement.

(credit to @serendipityhq for discovery)
(credit to anonymous user for helping me clarify some steps)
(credit to @SteemPoweredSweetheart for discovering all crew must be alive + loyal)

Deplorable
The worst fates.

Basically kill off everybody you can. See description for "An Ernest Attempt" in the previous section for more details as well, just do the opposite of that achievement for this one. I recommend disabling Decorum Game Overs in the Settings as well.

• Let the leopard seal kill Kurt's scout in Act 1;
  
• Let Dr Arthur leave the camp and die to the winter storm in Act 3 (do NOT say his father would be ashamed, otherwise he will stay just to spite you);
  
• Starve and freeze your crew with 0 rations for all of winter so everybody is extremely sick and close to death,
  
• Assign all the sick, wounded, frostbitten, and starving crew to Lifeboats 2 and 3, which causes Grimley and Junior to drown, along with everybody on their lifeboats;
  
• Shoot Cordell and Hammond when Cordell tries to escape in Act 4;
  
• Cut the rope when Kasha and Kurt try to recover Kasha's camera in Act 4.
  
• Ending choice doesn't matter AFAIK, I recommend abandoning the Viscount and seeking rescue so you can get "Comeuppance" below as well.

(credit to @Evan the Illiterate, PhD. for discovery)

Comeuppance
Meet Stanberry again.

You need to let Cordell keep Stanberry with her in Week 37 when you are leaving the dogs behind, kill Cordell, and then get marooned on the ice. Stanberry will eventually find you in the epilogue. I recommend disabling Decorum Game Overs in the Settings as well.

I got this by doing the same conditions as "Deplorable" above, and also choosing to abandon the Viscount mission so I could seek rescue instead.

• Templeton was disloyal so he and his scientists abstained when Appertton asked them to vote;
  
• Everybody else was dead so they abstained by default;
  
• Research wasn't mentioned at all since Kasha was dead, her camera was gone, and the scientists were disloyal, so I got 0 votes from research;
  
• Final tally was +0 (in favour) and -24 votes (abstained), so Appertton chose to leave me behind on the ice, and Stanberry found me in the Epilogue.

(credit to @Evan the Illiterate, PhD. for discovery)

Marooned
Get marooned, or maroon someone else.

I actually got this by choosing to maroon Hunt after winning the vote at the Viscount, but I chose to include it here because I think it combines well with "Deplorable" and "Comeuppance" above. You should get this by default with "Deplorable" since nobody votes for you and most of your crew is dead, while the rest are disloyal. You can also get this by marooning Templeton if he is disloyal, but only if you still win the vote at the Viscount.

Well, that's the end of the guide. Thank you for stopping by. I hope the descriptions and advice I've written help you out, and perhaps help you reach 100%.

It took a few dozen hours to test all the different events and endings, and it also took a few hours to write up, format, and edit this guide itself, so if you found this guide useful, kindly consider leaving a thumbs-up and favouriting.

Special thanks once again to users @serendipityhq, @criminalscum, @OkayCadet, @SteemPoweredSweetheart, @ChelsElixir, @riptrees, and especially @Evan the Illiterate, PhD, for assisting in discovery and testing.

Comments are welcome as well - if you notice I've missed something, made an error, or would simply like to ask for further details, please let me know. Thank you once again :)