Here is the full list of all 14 Check and Slash Demo achievements.
Defeat the White Knight Boss.
Destroy a White Queen.
Get +100 of Damage Bonus.
Get +50 of Damage Bonus.
Recover the lost damage bonus.
Get a attack recharge upgrade.
Die (and come back).
Defeat the White Pawn Boss.
Destroy a White Rook.
Destroy a White Bishop.
Destroy a White Knight.
Get a health upgrade.
Find a Black Piece.
Destroy a White Pawn.