Here is the full list of all 34 Choice Chamber achievements.
Complete a bridge that never goes back down
Receive 200% or more entries for a Gizmo
Possess 5 hearts at the same time
Defeat Roundleaf
Defeat a Totem without waking it up nor help from Gizmos
Possess only a Broken Heart
Defeat 5 or more enemies with a single attack
Kill a Bat with fire without attacking it
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
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 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
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
Get crushed by the final block in the Stack Room
Clear a normal room without attacking
Defeat every thing