Here is the full list of all 13 Pure Chess trophies - there are 9 bronze, 3 silver and 1 gold.
Achieve an ELO of 2500 or a Grandmaster Pure Chess rating.
Complete Tournament mode on all three difficulties.
Solve 100 mate problems.
Win a game of Play By Mail.
Perform a castling move on the queenside during any full game.
Perform an En Passant during any full game.
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.
Advance a pawn to the eighth rank in an offline game.
Win an exhibition game against the computer.
Put an opponent in check in an exhibition game.
Complete all the tutorials.