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