Here is the full list of all 35 Adventure Time: The Secret of the Nameless Kingdom achievements worth 1,000 gamerscore.
Chop down 999 bushes
Buy an item from Choose Goose
Find a Gum Globe
Get briefed on the mission
Find Lullaby Princess
Appease Cinnamon Bun
Find a renewable light source
Find Slumber Princess
Find Nightmare Princess
Locate the hidden Princess
Get Extra Ending 1
Get Extra Ending 2
Get the true ending
Find a Thump Shard
Max out your Thump Meter
Find every Baggy
Receive every type of Curse
Buy any variety of Trail Mix
Complete the Trading Game
Repair the wizard's door
Win the race against Starchy
Receive sword training
Complete the circle of love
Make a mess of the Pottery Shop until you get something nice
Find every item in the entire game.
Squash a Pie Fairy
Defeat an enemy after hitting it with both Finn and Jake
Use Flambo to defeat a Lub Glub
Shove a Fairy Convict into a Baggy
Find every secret Gunter cave
Dance the night away in the Rave Cave
Stun 5 enemies with a single Bananarang
Lie to Marceline
Attempt to speak to Stanley 5 times
Beat the game without upgrading Finn's Thumps, Sword, or Armor.