Here is the full list of all 35 Adventure Time: The Secret Of The Nameless Kingdom achievements.
Find a gum globe
Buy something from Choose Goose
Complete the tutorial
Complete the Song Temple
Complete the Cinnamon Fun! quest
Complete the Terrible People quest
Complete the Dream Temple
Complete the Fear Temple
Complete the Dungeon Drama quest
Choose Lullaby Princess to rule
Choose Slumber Princess to rule
Choose Nightmare Princess to rule
Find a thump shard
Find all thump shards / spare thumps
Find all five baggies
Receive every curse
Buy any trail mix
Complete the Trading Game quest
Complete the Door Repair quest
Beat Starchy's Graveyard Fun Run
Complete sword training
Complete the Love Note quest
Break the pot breaking record
Find everything in the game
Use Grabby Hand on a Pie Fairy
Kill an enemy after both Finn and Jake have attacked it
Kill a Lub Glub using Flambo
Store a Convict Fairy in a baggy
Find every Gunter cave
Party in the Rave Cave for 11 minutes and 12 seconds
Stun 5 enemies with a single Bananarang
Lie to Marceline
Talk to Stanley five times
Chop down 999 bushes
Beat the game with 3 thumps, without upgraded sword, shield, or armor