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.
Solve 100 mate problems.
Win a game of Play By Mail.
Complete Tournament mode on all three difficulties.
Perform an En Passant during any full game.
Win an exhibition game against the computer.
Put an opponent in check in an exhibition game.
Capture 100 pieces.
Deliver checkmate where the king is blocked on both sides by his own rooks.
Perform a castling move on the queenside during any full game.
Advance a pawn to the eighth rank in an offline game.
Deliver a check by two pieces at the same time.
Complete all the tutorials.