Here is the full list of all 13 Pure Chess Grandmaster Edition achievements.
Capture 100 pieces.
Complete all the tutorials.
Deliver checkmate where the king is blocked on both sides by his own rooks.
Perform an en passant move during any full game.
Advance a pawn to the eighth rank in an offline game.
Perform a castling move on the queenside during any full game.
Win an exhibition game against the computer.
Deliver a check by two pieces at the same time.
Put opponent in check in exhibition game.
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.