Here is the full list of all 28 Cross Set Infinity achievements.
Clear every 16 levels in first bonus level.
Complete Level 9.
Clear every level.
Complete Level 10.
Complete Level 8.
Reveal Level 10.
Complete Level 7.
Clear 109 standard levels.
Reveal Level 9.
Clear 9 random levels.
Clear 81 random levels.
Complete Level 6.
Complete Level 5.
Reveal Level 8.
Reveal Level 7.
Clear 73 standard levels.
Complete Level 4.
Reveal Level 6.
Clear one random level.
Reveal Level 5.
Complete Level 3.
Clear 37 standard levels.
Reveal Level 4.
Complete Level 2.
Reveal Level 3.
Complete Level 1.
Reveal Level 2.
Solve one level.