There are 6 Levels in Pumpkin Jack:

1. The Fields
2. The Haunted Mine
3. The Cursed Swamp
4. Skele-Town
5. The Spooky Cemetery
6. The North

There are 33 Achievements in Pumpkin Jack.

This section is for Miscellaneous Achievements.
Skull Breaker
Description: Send a monster back to the grave

Notes: This Achievement will be unlocked in the first few minutes of the Campaign. All you need to do is kill one of the Skeleton enemies that will spawn right after obtaining your first Weapon, the Shovel.
Shovel Face
Description: Equip the Legendary Holy Glory Shovel

Notes: This Achievement will be unlocked in the first few minutes of the Campaign. In The Fields Level, at the part where you use the Crow to kill 3 Skeleton Heads, there will be a Weapon, the Shovel, glowing in purple. Press the Use key (F by default) to grab it.
Fashion Victim
Description: Buy a new outfit!

Notes: The earliest you can buy new Outfits/Skins in the game would be a couple minutes after you find the first Weapon. You will find a skeleton mummy friend who wants you to buy his Skins in exchange for Crow Skulls. You can then also buy Skins in the Main Menu under Skin Selection.
Full Closet
Description: Fill out your wardrobe

Notes: This Achievement is unlocked when all Skins/Costumes have been bought.
Official Groupie
Description: Give in to your inner completionist

Notes: A Developer in the Pumpkin Jack Discord Server said that this Achievement is unlocked when getting all Outfits, all Skulls and all Gramophones.

This section is for Achievements that can be unlocked in Level 1 - The Fields.
Brand New Body
Description: Finish the tutorial

Notes: This Achievement will be unlocked in the first few minutes of the Campaign, in The Fields Level.
Crash Boo-ndicoot
Description: Smash all the crates in the fields

Notes: Fairly straightforward. Simply smash all the crates in The Fields Level.
Curse of the Scarecrow
Description: Kill the tyrannical Scarecrow and liberate the crows

Notes: This is the first Boss. You will encounter him towards the end of The Fields Level. He will do 3 moves. First, he'll be flying, throwing stuff at you. For this part, just keep running in a straight line, until you can attack him with the Crow. He'll go down, quickly get to him and spam you attacks on him. Then, he'll be doing ground stomps. Just keep jumping. Once that's done, 3 Skeletons will spawn, just kill them, then repeat everything until the Scarecrow is dead.

This section is for Achievements that can be unlocked in Level 2 - The Haunted Mine.
License to Drive
Description: Pass your abandoned minecart driving test

Notes: In The Haunted Mine Level, you will have 3 sections where you'll be riding a minecart. You'll obtain this Achievement once you pass the first section. It is located shortly after completing the first underground bomb-bouncing course.
Bomberman
Description: Complete all the underground bomb-bouncing courses

Notes: In The Haunted Mine Level, there will be 2 sections where you will need to push bouncing bombs to complete a puzzle. Complete both sections to unlock this Achievement.
Ghostbuster
Description: Kill the Phantom guarding the ancient mines

Notes: You will encounter this Boss towards the end of The Haunted Mine Level. He will start with ground stomps, just jump. After, he will shoot a laser at you, now run in big circles around him. Then, he will run at you in straight lines, just avoid these and keep running, while ordering your Crow to take out the small Ghosts at the same time. 3 Bombs will spawn, just choose one and hit it until it hits the Phantom. He will now repeat everything except now some platforms under you will disappear, making the fighting area smaller.

This section is for Achievements that can be unlocked in Level 3 - The Cursed Swamp.
Ghost Rider
Description: Ride the ghost horse all the way to the end

Notes: In The Cursed Swamp Level, there will be 3 sections where you will ride a ghost horse. Just finish one of those sections to unlock the Achievement.
De-Composer
Description: Make some magic mushroom music!

Notes: In The Cursed Swamp Level, there will be 2 sections where you will need to hit some mushrooms to make music. First, hit the one in the middle, listen, and repeat the same notes/mushrooms. Finish one of those sections to unlock the Achievement.
Cruel Tea
Description: Ruin the Witch and Merchant's cruelty-free dinner

Notes: You will encounter this Boss towards the end of The Cursed Swamp Level. The Witch will throw potions down at you from the top of the tree. Hit the green potions to throw them back at the glowing tree eyes to destroy them. Make sure you don't hit the red potions or they will just explode in your face. After destroying all the eyes, the bottom part of the tree will collapse. There will be spiked roots going in big circles, jump to avoid them while killing the branches that will attack you. Once those are all dead, the middle part of the tree will spawn glowing eyes. Repeat what you did with the green potions but be careful this time, the Merchant will be there to swing his whip at you. For the upper part of the tree, it's the same thing except the glowing eyes will move in circles around the tree. Once the tree is gone, hit the Witch and the Merchant multiple times to kill them.

This section is for Achievements that can be unlocked in Level 4 - Skele-Town.
Formula Ugh
Description: Beat the gate guards to the gate they guard on guard carts

Notes: In Skele-Town Level, there will be 2 sections where you will be racing city gate guards on carts. Finish one of those sections to unlock the Achievement.
Whack-a-Mole
Description: Win the game of Conveniently-Placed Hydraulic-Operated Underground Whack-a-Mole (patent pending)

Notes: In Skele-Town Level, there will be 2 sections where you will need to raise a lever in order to progress the game by hitting metallic rods with your pumpkin head. Finish one of those sections to unlock the Achievement.
The Bigger They Are...
Description: Be the David to Dhor's Goliath (i.e. kill the big guy)

Notes: You will encounter this Boss towards the end of Skele-Town Level. Dhor will start with a whirlwind attack going towards you. At this point, just run away from him. He'll then smash the ground so you can either jump or run away still. The city guards will come with a tower, kill those guards and bait Dhor to smash the tower filled with explosives, that will damage him. Next, a fire shower storm will happen, keep running to avoid them. The floor will then become red and some circle platforms will spawn, quickly jump on them to be safe from the lava. He'll throw hammers at you now so avoid them for a short while. The circle platforms will disappear but some lava cracks will stay on the floor now, avoid them. Repeat everything 2 more times to finally kill Dhor.

This section is for Achievements that can be unlocked in Level 5 - The Spooky Cemetery.
High Flyer
Description: Go for a nice walk with Abelard the Gargoyle

Notes: In The Spooky Cemetery Level, you will be transported by a Gargoyle and you will have to avoid obstacles. Finish this section to unlock the Achievement.
Ain't no rest for the wicked
Description: Clear away all those headstones cluttering up the graveyard

Notes: In The Spooky Cemetery Level, there is an area that will require you to destroy 16 tombstones in order to progress through the Level. Destroy them all to unlock the Achievement.
Hunger Killer
Description:
Solve world hunger (by killing Gluttony)

Notes: You will encounter this Boss towards the end of The Spooky Cemetery Level. Gluttony will start with a swing attack which you can just dodge to avoid. Right after, he'll summon waves of green flames. Just jump once for each wave to easily avoid them. He'll swing again so prepare to dodge. Now at this point he'll be summoning green goop skulls, kill them while avoiding Gluttony's contant knife throws. Once they're dead, dodge the next swing attack. After, 2 pillars will spawn. Hurry up, climb on one of them, and jump towards Gluttony to enter his vortex. You'll be inside Gluttony now and you'll see one flying green skull rushing towards you. Make sure you stand behind/in front of a pillar so it destroys it. Repeat to destroy all the pillars inside Gluttony. Once that's done, you'll be thrown out. Harmful green goop will spawn on the floor making the arena a bit more dangerous. Repeat everything 2 more times to finally kill Gluttony.

This section is for Achievements that can be unlocked in Level 6 - The North.
You'll Float, Too
Description: Reach the end of the vortex like a paper boat down a drain

Notes: In The North Level, you will have to go through 2 Vortexes and you will have to avoid obstacles and use the Crow to kill Skeletons. Finish one of these sections to unlock the Achievement.
The Worst Achievement Possible
Description: Get on Santa's Super-Duper-Duper-Naughty List

Notes: In The North Level, there will be 2 sections where you will have to kill Santa Claus by pushing presents towards him with your pumpkin head. Finish one of these sections to unlock the Achievement.
The Baddest Bad Guy
Description: Kill the Wizard + Get the Amulet = Profit

Notes: You will encounter this Boss towards the end of The North Level. The Wizard will start by spawning lightning from the sky that will hit the ground at multiple spots. While this is happening, he'll also spawn electricity bubbles that will chase you, make sure you destroy them with the Crow. After a bit, he'll summon large tornadoes that will chase you, again with the chasing electricity bubbles. Once they disappear, he'll make huge walls that will come down towards you with a hole in the center. Make sure you go through the holes. After the last wall, he'll be channeling energy to himself for a big attack. Destroy the 4 altars around him to prevent that from happening. Quickly, hit him! Once enough damage has been dealt to him he will make the arena smaller. Repeat everything 2 more times to kill The Wizard.

This section is for Achievements that will require you to find Gramophones and Crow Skulls throughout the Levels. Once you find a Crow Skull within a Level, you keep it forever, meaning you do not have to find all of them in a single playthrough.
Prying Eyes
Description: Pick up a crow skull

Notes: Crow Skulls are Collectibles. There are 20 Crow Skulls per Level. Some of them are very obvious, while some others you will need to explore a bit more to find them.
You've Got A Problem, Man
Description: Collect every single crow skull in the world

Notes: There is a total of 120 Crow Skulls. Follow the videos down below for Walkthroughs.
Boogie-Man Wonderland
Description: Find a gramophone and DANCE, DANCE, DANCE!

Notes: Gramophones are Collectibles. There is 1 Gramophone per Level. They are usually cleverly hidden.
Disk Jockey
Description: Make vinyls cool again. ...Actually, that's impossible, even as a joke. Just find all the gramophones.

Notes: There is a total of 6 Gramophones. Follow the videos down below for Walkthroughs.
Skull Finder
Description: Collect all crow skulls in the fields

Notes: You will need to collect all 20 Crow Skulls in The Fields Level
Skull Hobbyist
Description: Find all crow skulls in the ancient mines

Notes: You will need to collect all 20 Crow Skulls in The Haunted Mine Level.
Skull Collector
Description: Collect all crow skulls in the swamp

Notes: You will need to collect all 20 Crow Skulls in The Cursed Swamp Level.

Skull Aficionado
Description: Collect all crow skulls in Skeletown

Notes: You will need to collect all 20 Crow Skulls in Skele-Town Level.

Skull Fanatic
Description: Collect all crow skulls in the graveyard

Notes: You will need to collect all 20 Crow Skulls in The Spooky Cemetery Level. You will have to spend a couple Crow Skulls towards the end of the Level, but don't worry, it won't deny you the Achievement.

Skull Obsessive
Description: Collect all crow skulls in the North

Notes: You will need to collect all 20 Crow Skulls in The North Level.