Overboard! has a lot of moving parts and a tight schedule, so it's obvious why someone would get stuck. In this guide, a general walkthrough will be given, as well as more focused ones for individual achievements.
I'd advise making a good old college try to understand the game, as figuring out what to do is most of the fun. There's one section of this guide with no explicit information to help you get the basics, but beyond that, the game will be laid bare. Please proceed with caution.

• Keep your story straight. Contradicting yourself will instantly make you suspicious in the meeting. For example, in my first playthrough, I told everyone I met that my husband was dead… except for Clarissa, who I tried to calm down by saying he was still alive. This blew up in my face in the meeting, where she pointed out that I lied to her and tanked my case. Almost everyone asks where your husband is when you talk to them, so be very careful to give a consistent answer. Similarly, be careful when people ask about your earrings, because Carstraight asks multiple questions and it's easy to slip up. ( I once told him they weren’t my earrings and then alleged that Clarissa stole them from me. I was predictably arrested.)
  
• Similarly, keep your nose clean. Being caught breaking in to a cabin or threatening people willy nilly will tank your credibility.
  
• Make a plan in advance. Before a run, sit down and think about what outcome you want, and what you would need to do and when those tasks need to be done by, so you don’t get blindsided. I’ve screwed up multiple runs because I forgot to grab my sleeping pills or Clarissa’s cabin key until it was too late.
  
• You can head to the Chapel and ask God for help at any time. They’re a little vague, but any hints are welcome.
  
• The actions taken in your last COMPLETED run are saved for future runs. For example, if you can convince Clarissa to talk with you on the Upper Deck, what you said to convince her will be saved for the next run. This allows you to skip parts you have down pat, which can save you some time. “Completed” is emphasized, as resetting to 8 AM will revert to the last saved choices, instead of the ones you made in the reset run.
  
• Ringing the Bell on the map instantly cuts to the meeting. If you have everything in order for the meeting, you can save some time by ringing the bell. Also, this is an integral part of speedrun achievements, so you don’t have to wait 15:00.
  
• Since this game is nonlinear, there are multiple valid ways to play and get the same ending. If your route or schedule doesn't exactly match up with mine, then no worries!

This game uses military time, so this guide will too. Now, you have seven actual hours to plot and a one hour meeting (the game starts at 8:00 and the passenger meeting starts at 15:00). The times are a little inexact, e.g. I put down Carstairs as arriving on the Upper Deck at 8:30, but I have seen him arrive there at like 8:33 when I went to grab my earring, so be careful. Also, if you are in an area when people move around, there’s unique dialogue when they leave or enter (If you’re in the cabin hallway, Clarissa will shove you out of the way sobbing when she arrives at 9, and Major Singh will introduce himself and walk off at 10)

8-9:00 Cries in the Restaurant
9-15:00 Cries in her cabin
Whenever she’s in her cabin, you can convince her to talk with you on the upper deck, which will give you a brief window to break into her room or meet with her on the deck, or both. This trick can be pulled multiple times in one attempt

8-8:30 In his cabin
8:30-9:20 Doing a lap of the upper deck. Note: If you haven’t retrieved your earring before this point, he has it now, and you must deal with this setback.
9:20-11:30 Playing cards in the Smoking Room, and can be gambled against for money.
11:30- 12:30 On Upper Deck
12:30-15:00 Back to cards in the smoking room
At any time, if you’ve figured out the stowaway, you can blackmail him about her. This can be done by either heading to his cabin first thing and eavesdropping, or learning the knock from Lady Armstrong and checking yourself. It will also change his Upper Deck conversation to him threatening you, which can be used to kill him

8-8:20 On Upper Deck, but he leaves so quickly you can’t possibly catch him
8:20-10:00 In his cabin, will eavesdrop on any conversation with Clarissa
10-15:00 In the Smoking Room. At 15:00, he will notice that Malcolm is missing and initiate the meeting.
If Carstairs vanishes overboard, then Singh will eventually notice. If you’re in the smoking room, at around 12:30 Singh will ask where Carstairs went, and you can tell him to search the deck. The Major will then head up there and can be killed off.

8-8:30 Breakfast in the Restaurant
8:30-9:40 In her cabin
9:40-11:00 On Upper Deck
11:00-11:25 In the chapel, praying. If followed into the chapel and eavesdropped upon, she’ll leave behind 200 pounds in the Alms tray
11:25 - 13:30 Drinking in the Restaurant. This is your window for drugging her with a sleeping pill.
13:30-15:00 In her bedroom, sleeping. Vulnerable
You have a limited amount of time to learn about Carstair's knock or to buy the blackmail off her, as she can't be spoken to after she goes to bed.

8-8:30 Breakfast in the Restaurant
9:00-11:00 in the Bridge
12-5:00 In the Bridge, again
During breakfast or his first Bridge shift, you can set up an 11:30 tryst with him. This initiates the romance and allows you to steal his pass key, but if you miss the meeting, he will refuse to talk to you for the rest of the attempt.
Generally, if you upset him (Miss the tryst, kill the steward, blackmail him), he'll refuse to talk to you for the rest of the run.
Also, if he’s on shift in the Bridge, you can throw someone off the Upper Deck without an instant game over!

Your husband’s jacket, with his wallet and Clarissa’s key, can be found in the Smoking room. At a little before noon, a worker will move the jacket to your cabin... but will steal the wallet.
A maid will enter your bedroom at 10:30-ish. If something incriminating, like a corpse or the sleeping pills, is present at that time, it will be brought up during the meeting. However, if you're there when she enters, you can demand she leave, so that she won't see anything incriminating.

• The game has three tiers of endings: Freedom (Not arrested), Money (Got someone else arrested for the murder), and No Loose Ends (Got Lady Armstrong arrested for murder).
  Broadly speaking, if the evidence is inconclusive in the meeting, they will default to “Your husband committed suicide,” which earns you Freedom.
  The various speedrun achievements all have different ending thresholds, so please keep an eye on what they want, e.g. Smooth Operator and Fast Work only need you to avoid arrest and get Freedom, while Storm/Tornado Protocol have you do the whole monty and get No Loose Ends
  
  
• Anders is your accomplice, and will lie for you in the meeting. For example, if you’ve planted evidence to make Clarissa look suspicious and you’re not too suspicious, he’ll lie and say he saw her do it. This does not apply to Lady Armstrong, as she has blackmail on him, and you need to retrieve the blackmail photo for him to go along with framing her.
  
  
• Leaving your sleeping pills in your room is always a bad idea, as someone will find it and dismiss you as hysterical.
  
  
• The meeting follows a pretty stable rhythm: Clarissa claims you killed him and swears she saw your husband fall overboard last night, Lady Armstrong says she saw a woman with him before he fell overboard, Carstairs presents the earring, and so on. When thinking of what to do, consider this, as manipulating or killing certain people can simplify the trial.
  For example, if you kill Carstairs, he won’t present the earring. If Clarissa is convinced to confess, the meeting will end when she first talks.
  
  
• There are a boggling amount of ways to correctly or incorrectly handle a specific problem.
  For example, one problem you face is that you lost your other diamond earring on deck when you pushed your husband overboard, and if not nipped in the bud, this will tie you to the crime scene.
  Successful ways to handle it include: Rush to the Upper Deck before 8:30 and retrieve the other earring, pocket your earring at your cabin bathroom mirror and tell Stairway that the one he found isn’t yours, learn Stairway’s secret and blackmail him into silence, kill Stairway, and planting your earring in Clarissa’s cabin so it connects her to the crime scene.
  Unsuccessful ways to handle it include: giving a contradictory story, lying that the other earring is glass (Singh will see through you), saying you lost your earring the day before (Stairway will say there was a storm and it would have been lost), being seen by Lady Armstrong or Stairway with one earring and then arguing it’s not yours.

In this section, what needs to be done for each ending will be laid, along with some possible approaches.

There are two incriminating pieces of evidince that will sink your credibility: the sleeping pills and the missing earring. With them out of the way, you can easily play your husband's death off as a suicide.
The Sleeping Pills: they are in your cabin bathroom. If found, the steward will write you off as insane during the meeting.

Ways to handle this:
• Pocket them
  
• Have the trial end quickly, e.g. nobody will ask you if Clarissa confesses
  
• Plant them in Clarissa's room

The Earring: When you murdered your husband, one of your two diamond earrings fell out on the Upper Deck. At 8:30, Carstairs will find the other earring. This is a problem, as it ties you to the crime scene.
Ways to handle this:

• Rush to the deck and put grab the earring before Carstairs gets there
  
• Remove your earring in your bathroom mirror, and convince Carstairs that it doesn't belong to you
  
• Murder Carstairs by throwing him overboard
  
• Find out about Carstairs' secret, which means learning the special knock from Lady Armstrong and checking his cabin. When he brings up the earring in the meeting, break out the blackmail and silence him.

Additionally, while not necessary to do, if Clarissa falls overboard, the meeting will quickly conclude that it was suicide pact, as Clarissa is the only person to blame you. Either of the methods in the Additional Murder section can achieve this goal.

Clarissa needs to be arrested, and there are many ways to do that.

• Enter her room with either the key from your husband's jacket or the pass key and plant evidence. The sleeping pills will make her look unstable, while your husband's wallet will prove that she met him before his death. With these down, you can blame her, and Anders will back you up.
  
• Make her confess of her own free will. Take a love poem from her desk and start talking to her. Show the poem to her. Claim that your husband gave it you before he jumped. Clarissa will think she made him kill himself and confess in the meeting.

The blackmailer is Lady Armstrong, so framing her for the murder kills two birds with one stone. However, she has ironclad blackmail on Anders in her cabin. You need to deal with that to frame her.

• You can use the pass key, obtained either by swapping it with Clarissa's after the tryst with Anders or taking the key from him in the bridge, to enter her cabin and take it.
  
• If you drug her with a sleeping pill, you can walk her to her cabin and take the picture. Grab the sleeping pills, head the restaurant, and talk to her in the afternoon. Order a drink and distract her with sad questions. Swap your drinks once, and then drug your drink before swapping a second time. She'll feel sleepy, and you can walk her to her cabin for access.
  
• You can buy the picture from her, but it is 1000 pounds. To obtain the money: start the card game with Carstairs without money, and he'll trade 500 for your diamond earring. Grab your husband's wallet from his jacket for 400 more. Finally, enter the chapel when Lady Armstrong is there, and spy on her. When she's done praying, she'll leave 200 pounds in the alms tray you can take. With 1100 pounds total, you can buy the picture from her.

Alternatively, if the Lady dies, she can't blackmail you. This one is a little strict, as, in most situations, if she dies, it will instantly be pinned on you.

• The one exception is if she dies in the same run that Clarissa confesses for the murder in, which means that the meeting is cut short with no questioning. Show Clarissa the love poem to make her confess, get the pass key from Anders, and smother her with a pillow in the afternoon. ( Thanks to @34Witches for pointing this out!!)

These achievements will be gotten at the ending.

Banged Up: Lose an attempt and get arrested. You’ll get it sooner or later.

Escaped Justice: Basic ending. Have the meeting play out without being caught, either through a lack of evidence or playing the death as a suicide.

Make a Killing: Insurance payout ending. Get someone else, such as Clarissa, taken away for the murder.

No Loose Ends: Best ending. Have Lady Armstrong taken away for murder so she can’t blackmail you. For this route, you need to get your hands on the blackmail photograph she keeps in her room, give it to Anders, and then pin the murder on her in the meeting.

Hooked Up: Get away with murder and end the game with Anders as your lover. This will trigger at the credits. Assuming you don’t blackmail him or drive him away, you’ll be together.

These achievements require to complete a feat of some sort during your run.

Reunited!: Throw yourself overboard. Available at any time, but will end your run.

Take the Wheel: Meet Anders in the Bridge during his morning shift and ask “Can I try the wheel?” The two of you will have a cute bonding moment and earn an achievement.

God: I Hate Poetry: Enter Clarissa’s cabin and steal a love poem from her desk. Then, head to the Chapel and talk to God. There will be an option to start riffing on her poems with God, which will net you the achievement.

It’s All Over: Throw all of your husband’s possessions out the cabin porthole. Head to the smoking lounge and grab his wallet and the key to Clarissa’s cabin. Then, break into Clarissa’s room and check her nightstand, as your husband left a book there. With the book in hand, return to your cabin and head to the porthole. Throw the book, his wallet, and finally his clothes through the porthole for this achievement.

Liaison Officer: Sleep with Anders. Talk with him in the morning before 11:00 and set up the 11:30 tryst in your cabin. Be there on time to romance him and get the achievement.

Tighten the Knots: Blackmail someone. I got it by learning about Stairway’s stowaway, and when he shifts blame on you during the meeting, threaten him into silence. In my run, Stairway brought up my missing earring, and I then said “I’m not the woman you should be worried about,” which will make him drop it and earn the achievement. I assume from the icon that you can do a similar thing with the blackmail photograph and Anders, but I do not know. I would love confirmation or feedback on this.

Leap of Faith: Make Clarissa jump from the Upper Deck. Run to the Smoking Room and grab Clarissa's room key from your husband's jacket. Then, rush to her cabin, break in, and grab a love poem from her desk. When Clarissa arrives, talk her into meeting on the Upper Deck.
During the conversation, show her the love poem and say your husband gave it you, and that you laughed about it together. You can then cruelly torment Clarissa until you "You never stood a chance against me," which will drive her to suicide.

Sleep Well Dear: Drug Lady Armstrong with a sleeping pill. Take the pills from your cabin bathroom, and wait in the Restaurant for the Lady to come in for a drink. Order a drink of your own and palm a sleeping pill. Whenever you ask her a sad question, like if she's married or if she has kids, she'll dramatically wipe her eyes with a handkerchief, which means you can tamper with her drink. If you drug her drink, she'll notice the pill and order another. If you swap drinks, she'll spit yours out.
The trick is to swap your drink, then place a pill in your own and swap it with hers. If she drinks twice from your glass, she'll assume it was hers all along and swallow the sleeping pill. This allows you to drug her and walk her to her cabin, which can be used to kill her or grab the blackmail photo.

Take the House : Rob Carstairs blind in his card game.
Figure his secret (either learn the knock from the Lady and try it on his door or arrive at his cabin before 8:30) and threaten Carstairs with it. When you start the game of cards, tell him you want a Pontoon, the best possible hand that earns you double, and bet three hundred pounds. (Thanks to @Alphadoriest for pointing this out!!)
Now, I got the blackmail and earned 600 pounds several times without the achievement triggering. The run that got me the achievement, I grabbed my earring, the blackmail, but not the wallet. After threatening Carstairs, I traded an earring for 500 pounds, before threatening him for the pontoon and another 600. He had different dialogue, about how I cleaned him out as opposed to him having bet enough, and the achievement popped up.

The Double through Septuple Homicide achievements follow a similar path: starting with one death (as you already killed your husband), kill additional people for the achievement. Kill one person for Double Homicide, two people in one run for Triple, all the way up to killing six people in one run for Septuple homicide. Mind you, there are only six other people on the ship, so a Septuple Homicide run will kill everyone on board.

Possible Murders
The Steward: At the beginning of a run, invite him indoors and ask for “One more thing,” then select the “Conk him on the head” option. This will kill him, and you’ll waste thirty minutes hiding the body. Before you hide the body, check under the bead for his pass key. Note: the body will be found at the meeting and instantly get you arrested, unless you set up the tryst with Anders and used him to get rid of the body.

Lady Armstrong: Through any means (Pass key/drug her cocktail and walk her to her room), enter her cabin in the afternoon. You have the option to observe her and then smother her with a pillow (one push if she’s drugged, three if she’s sober). Note: this will also get you arrested, as the maids will find her dead later.
Alternatively, if you murder Clarissa right in front of her, you can lure her into looking over the railing and push her over! (The text options are “Can you show me where she went over?” and then “Push her over”)
Clarrissa: Head to her cabin and convince her to talk with you on the Upper Deck. On the deck, there are multiple paths the conversation can take that can lure her to the edge. An early one is to ask if she sees dolphins. Another is when you ask what she saw, there’s an option to ask “Is that your porthole down there?” The followup option, “You can join him, Clarissa” then murders her. Note: if there are no witnesses and Anders is on duty, then you’ll get away scot free.
Alternatively, grab a love poem from her room and meet her on deck. Through the same actions as the Leap of Faith achievement, you can drive her to suicide.

Carstairs: When he’s on the Upper Deck, you can lure him into watching the dolphins and push him overboard.
Alternatively, if you’ve blackmailed him over the stowaway, he’ll pull a gun on you when you talk on the Upper Deck. If you get close to him and pull the trigger, he’ll get shot and fall overboard. Note: assuming Anders was on duty, there will be no evidence and no one will seriously comment on his disappearance.

Major Singh: First, murder Carstairs. Singh will eventually notice that he’s gone and will ask if you’ve seen him. If you tell him that Carstairs might be on the Upper Deck, then Singh will head up there and look over the rail. Grab the knife from his belt and push him overboards. This one takes some time, as he grabs hold of the rail and you pry his hand open. Anders will see you and immediately try to have you arrested.

Anders: Murder Singh, and Anders will insist on arresting you. Grab the knife and deliver a super villain monologue before stabbing him, and he’ll take you over the rail with him.
I don’t know if it’s possible to kill him during the tryst. He caught my arm every time I tried. Does anyone have confirmation on this?

Now, let’s put it all together.
Lure the Steward into your room and cosh him over the head. After hiding the body, go to the bridge and stall until Anders comes in at 9:00. Head to the Upper Deck and make Carstairs watch the dolphins before pushing him overboard. Head to Clarissa’s cabin and convince her to talk on deck with you. On the upper deck, throw her overboard, and when Lady Armstrong confronts you, kill her next. Head to the Smoking Room and wile away the hours until 12:30, when the Major asks you where Carstairs is. Send him up to the Upper Deck and follow him there. Take the knife from his belt, stab him in the back, and pry his fingers from the rail. When Anders comes to arrest you, talk until you can grab the knife and kill him. Sit back and watch the strange ending.

These one require you to get a certain ending in a certain amount of time. Keep in mind you can ring the bell or talk to Major Singh to start the meeting early and that meeting does take up time. For example, if you start the meeting at 10:30 (two and a half hours), then the meeting will likely end closer to 11.

Smooth Operator and Fast Work: Don't get arrested in under 5/3 hours. The easiest one to get, as the meeting defaults on this conclusion if there's no evidence linking you to the scene. There's a lot of room for error, so don't feel pressured.

Wake up and grab your sleeping pills. Rush to the Upper Deck and grab your earring. Then, head to the bell. We're going to pass it off as a suicide. In the meeting, don't point fingers at anyone and allege that he committed suicide in the night. Major Singh will ask if you killed him, and, surprisingly enough, he'll buy it if you say no.
Excellent Execution and Fast Finagling: Frame someone for murder in 5 hours, or 2 hours (!!!!!!!). The second one is very, very strict.
Run to the Smoking Room and grab Clarissa's cabin key from the coat. Head to her cabin, grab a love poem from the desk, and exit the cabin. Wait in the hall until Clarissa arrives. Show her the poem and tell her that "He gave it to me before he jumped." Clarissa will think she killed him, and will confess without arguing. Knock on Major Singh's door and say that your husband fell overboard. The meeting will rapidly play out with Clarissa confessing.

Storm Protocol and Tornado Protocol: Pin it all on Lady Armstrong, and do it in under 5/4 hours. This is easier than you would think.

Wake up, yell at the steward, and grab your pills. Run to the Upper Deck and grab your earring. Wait until Anders walks past and follow him up the the Bridge. There's an oddity here where Anders won't talk about the pass key if you're in the bridge when he enters, but he will if he's already there. Talk to Anders until the Pass Key option comes up. Seduce him for the key, and head for Lady Armstrong's cabin. Go the the bookself, open The Nine Tailors, and grab the blackmail photo. Head back to the bridge and give Anders the photo. Ring the bell and start the meeting. Steer the conversation towards incriminating the Lady and let Anders take her down. I rung the bell at 11:12 and the meeting ended with ten minutes to spare.