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