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.
Complete Tournament mode on all three difficulties.
Capture 100 pieces.
Deliver a check by two pieces at the same time.
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.
Perform an En Passant during any full game.
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.
Win a game online.