Here is the full list of all 34 Choice Chamber achievements.
Receive 200% or more entries for a Gizmo
Defeat Roundleaf
Kill a Bat with fire without attacking it
Complete a bridge that never goes back down
Defeat Starnose
Defeat Jellyball
Defeat Alpha
Defeat Babblon
Possess 2 spiked hearts at the same time
Progress through 10 consecutive rooms without pressing jump
Progress through 10 consecutive rooms without running left
Defeat 5 or more enemies with a single attack
Complete the game without warps or shortcuts
Complete the game in 15 rooms or less (chest and shop rooms don't count)
Possess 5 unique hearts at the same time
Possess 10 unique hearts at the same time
Possess 5 hearts at the same time
Possess 10 hearts at the same time
Defeat a Boss without attacking nor help from Gizmos
Unlock Max
Unlock Lucky
Exit through a door before defeating all enemies
Purchase 2 items in a shop
Purchase all 3 items in a shop
Defeat a Totem without waking it up nor help from Gizmos
Be surrounded by 5 or more Gnats at the same time
Defeat a divekicking Diver with 1 heart left
Bounce a ball on your head 25 times in a row
Bounce a ball on your head 50 times in a row
Possess only a Broken Heart
Get crushed by the final block in the Stack Room
Clear a normal room without attacking
Defeat every thing