Here is the full list of all 20 Crystal Crisis achievements.
Beat the game with all the female characters
Win a round with your grid at least 90% full
Beat the game with Aban, Jim and Tina
Detonate a Cluster with at least 18 Crystals in it
Beat the game with Astro Boy, Curly, Ninja and Quote
Perform a quad-crystal combo
Perform a quin-crystal combo
Detonate a Cluster with at least 12 Crystals in it
Beat the game with Astro Boy and Black Jack
Perform 10 different bursts
Detonate a linked chain of 20 or more Crystals
Perform a tri-crystal combo
Detonate a linked chain of 10 or more Crystals
Complete the tutorial twice
Play an online match with a friend
Win 10 ranked online matches in a row
Win five ranked online matches in a row
Win two ranked online matches in a row
Win a match without ever rotating a Crystal pair
Play a ranked online match