Here is the full list of all 36 Adventure Time: The Secret of the Nameless Kingdom trophies - there are 20 bronze, 11 silver, 4 gold and 1 platinum.
Earn all trophies in the game.
Beat the game without upgrading Finn's Thumps, Sword, or Armor.
Get Extra Ending 2
Get the true ending
Get Extra Ending 1
Attempt to speak to Stanley 5 times
Shove a Fairy Convict into a Baggy
Stun 5 enemies with a single Bananarang
Dance the night away in the Rave Cave
Find every item in the entire game.
Max out your Thump Meter
Receive every type of Curse
Complete the Trading Game
Find every Baggy
Repair the wizard's door
Make a mess of the Pottery Shop until you get something nice
Locate the hidden Princess
Find Nightmare Princess
Defeat an enemy after hitting it with both Finn and Jake
Use Flambo to defeat a Lub Glub
Lie to Marceline
Receive sword training
Find every secret Gunter cave
Win the race against Starchy
Find Slumber Princess
Find a renewable light source
Appease Cinnamon Bun
Find Lullaby Princess
Squash a Pie Fairy
Complete the circle of love
Find a Thump Shard
Chop down 999 bushes
Buy any variety of Trail Mix
Find a Gum Globe
Buy an item from Choose Goose
Get briefed on the mission