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