Here is the full list of all 16 Cthulhu Saves Christmas achievements.
Defeat the 1st League of Christmas Evil member.
Defeat the 2nd League of Christmas Evil member.
Defeat the 3rd League of Christmas Evil member.
Defeat the 4th League of Christmas Evil member.
Defeat the 5th League of Christmas Evil member.
Defeat the 6th League of Christmas Evil member.
Defeat the 7th League of Christmas Evil member.
Complete the game.
Recruit the Snow Maiden, Crystal Claus.
Recruit the witch, Baba Yaga-chan.
Recruit the old man, Belsnickel.
Use the battle command.
See a familiar face.
Fill all 4 item slots with an item.
Forge an unbreakable R'lyehtionship.
Use a unite ability at 100% power.