Here is the full list of all 46 Adventure Time: Explore the Dungeon Because I DON'T KNOW! achievements.
Fully upgrade LSP.
Fully upgrade Jake.
Fully upgrade Ice King.
Fully upgrade Cinnamon Bun.
Survive 50 Floors in one Nightosphere run.
Survive 25 Floors in one Nightosphere run.
Fully upgrade Lemongrab.
Survive 15 Floors in one Nightosphere run.
Fully upgrade Flame Princess.
Find all of BMO's Game Cartridges.
Complete all of Princess Bubblegum's Quests.
Complete all of Starchy's Quests.
Collect every Token.
Fully upgrade Marceline.
Uncover Bubblegum's dark secret.
Collect every Sub-Weapon.
Complete all of Susan Strong's Quests.
Overcome the Guardians' punishment.
Fully upgrade Finn.
Complete all of Mr. Pig's Quests.
Free Flame Princess.
Enter the Nightosphere.
Complete all of Tree Trunks' Quests.
Free the Earl of Lemongrab.
Survive a Monster Floor
Locate every Familiar.
Weather Goliad and Stormo's psychic assault.
Rescue the Hyoomans.
Grab 50 Treasures on a single Treasure Floor.
Upgrade a Sub-Weapon into a stronger one.
Assist Gunter with a feisty feline.
Eat every Food item at least once.
Put Ice King in his place.
Upgrade a character's Focus.
Upgrade a character's Imagination.
Outrun the stampeding prisoners.
Receive a Curse.
Buy something from the shop.
Pick up every Item pickup at least once.
Upgrade a character's Rowdiness.
Outsmart the Demon Cat.
Upgrade a character's Thumps.
Return from the Dungeon alive.
Complete a Quest for the Princess.
Use a Special Attack.
Perform a Perfect Block.