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