Here is the full list of all 22 Dark Snow achievements.
Begin New Game
Complete level 1
Complete level 2
Complete level 3
Complete level 4
Complete level 5
Complete level 6
Complete level 7
Complete level 8
Complete game on Dream difficulty
Complete game on Nightmare difficulty
Complete game on Coma difficulty
Found the key
Found Teddy Bear
Destroy Ice Sphere
Free 6 lost souls
Free 66 lost souls
Free 666 lost souls
Kill 6 demons
Kill 66 demons
Kill 666 demons
Fill Demon King