Here is the full list of all 36 Adventure Time: Pirates of the Enchiridion trophies - there are 20 bronze, 10 silver, 5 gold and 1 platinum.
Collect all trophies
Pull the plug!
Complete all side quests
Take all the penguins to the tree house
Light all the braziers in the Fire Kingdom
Get Finn to level 10
Get Jake to level 10
Get Marceline to level 10
Find the snail
Free the caged Mushroom people
Restore light to the treasure tree
Get BMO to level 10
Dock at all the islands
Beat Uncle Gumbald in battle
Inflict more than 1 bunk effect on to a single enemy
Beat the Fire Giant in battle
Use BMO's Analyze.exe
Beat the Mother Varmint in battle
Overskronk 4 enemies in a single battle
Use all the pirate lookouts
Unlock a gate with BMO
Open 15 treasure chests
Beat 50 enemies in battle
Beat Fern in battle
Complete your first side quest
Buy your first item from the shop
Destroy 250 land destructibles
Win your first fight against a higher level enemy
Revive a hero
Fall in to water more than 10 times
Destroy 10 Sea destructibles
Fish out 25 items from the sea
Destroy 50 land destructibles
Use a pirate lookout
Win your first sea battle
Pass the first Interrogation