Here is the full list of all 13 Super Puzzle Sisters achievements.
Play match with four Persimmon
Win with grid almost full
Lose after having 20% more points of the opponent
Lose without touching a single button
Win using only defense specials
Win without making a single combo
Win without using a single special
Perform x9 combo
Mute Music
Get a 40000 Points in Wide Mode
Get a 30000 Points in Endless Mode
Get a 20000 Points in Time Attack
Complete tutorial