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