Here is the full list of all 27 Squarism achievements.
Breached
Finish 20 levels
Sticked
Complete level with that huge 4x4 square
Finish 10 levels
Complete level after 5 restarts
Fail level 3 times
Make wrong shape
Complete tutorial levels
Use restart
Complete first level
Finish 30 levels
Finish 40 levels
Finish 50 levels
Finish 60 levels
Solve last level
Solve everything
Destroy your only movable shape
Use restart 10 times
Spend 5 minutes solving single level
Spend 20 minutes solving single level
Spend 3 minutes in level selection menu
Hivemind
Opened
Guided
Sacrificed
Spend 5 wonderful minutes in credits menu