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