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.
Win an exhibition game against the computer.
Solve 100 mate problems.
Perform a castling move on the queenside during any full game.
Deliver checkmate with a pawn.
Put an opponent in check in an exhibition game.
Perform an En Passant during any full game.
Complete all the tutorials.
Complete Tournament mode on all three difficulties.
Capture 100 pieces.
Advance a pawn to the eighth rank in an offline game.
Win a game of Play By Mail.
Play a check in reply to a check.