Here is the full list of all 12 Puzzle & Chess achievements.
Level 10 completed !
Level 20 completed !
Level 30 completed !
Level 40 completed !
Complete level 37 without viewing the lines
First level completed !
Do a wrong movement
kill an enemy piece
Lost a piece to enemy
Unlock a piece
Transform a pawn in an another piece
Complete level 26 without click on restart