Here is the full list of all 24 Adventure Time: Finn and Jake Investigations achievements.
Free Abracadaniel from jail.
Use all four Jake combat forms at least once in the game.
Perform a 15-hit combo in combat without being hit.
Visit every area in and around the tree house.
Use the telescope in the boat to look at three different kingdoms.
Find a way to get into the wizard "party."
Defeat the wizards and free the kidnapped Candy People.
Find the hairy beast that has been wreaking havoc.
Fix all of the noble deeds that were done incorrectly.
Put the king back in charge of his kingdom.
Find a cure for the dancing epidemic.
Find the missing Sound Sword.
Defeat Magic Man's latest jerky plan.
Find out why the Fire Kingdom's flames are going out.
Escape from the dungeon below Billy's Cave.
Find the last of the artifacts and seal Billy's Cave.
Gather the equipment needed to re-record Finn's record.
Convince Finn's friends to join the band.
Put Finn's favorite song back onto the record album.
Correctly guess the Grayble theme.
Locate and interact with 15 snails.
Dial 10 wrong numbers on the pay phone.
Listen to all of the radio broadcasts in the Tree House bedroom.
Say hello to the new character in Ooo.