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