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