Here is the full list of all 13 Pure Chess Grandmaster Edition achievements.
Deliver checkmate where the king is blocked on both sides by his own rooks.
Deliver a check by two pieces at the same time.
Capture 100 pieces.
Perform an en passant move during any full game.
Perform a castling move on the queenside during any full game.
Advance a pawn to the eighth rank in an offline game.
Win an exhibition game against the computer.
Put opponent in check in exhibition game.
Complete all the tutorials.
Win a game of Online Play.
Complete Tournament mode on all three difficulties.
Solve 100 mate problems.
Achieve an Elo of 2500, or a Grand Master Pure Chess rating.