Here is the full list of all 30 Caverns of the Snow Witch achievements.
Remember an old legend to your benefit
Shatter the Crystal Warrior into pieces
Consume ten of your Provisions
Try all three of the rings
Hit the true Illusionist on your first try
...even if it's not your birthday
Find the ultimate ending in Hardcore mode
Find the ultimate ending in Medium mode
Find the ultimate ending in Free Read mode
Find all the images hidden within Caverns of the Snow Witch
The Snow Witch is Dead!
Survive your own murderous hand
Receive a curse from a stranded Dwarf
Fly on a Pegasus
Trick two foolish Goblins
Survive being swept up by an avalanche
Steal a boat and sail away
Deny the Brain Slayer of a meal
Steal a meal of duck
Slay the zombie replicas of your friends
Be healed by the minstrel's music
Successfully navigate your way past the Banshee
Solve the riddle of the rhyme
Find all enemies with these words in their name
Find all three metal shapes
Beat the Snow Witch at her own game
Experience a particularly nasty shower
Read the spell on the scroll before it fades away
Take all of the Snow Witch's treasure
Convince the centaurs that you have nothing of value