There are 9 Bronze Trophies, 3 Silver Trophies, and 1 Gold Trophy.
Amateur (Bronze) - Complete all the tutorials.
Check (Bronze) - Put an opponent in check in an exhibition game.
Checkmate (Bronze) - Win an exhibition game against the computer.
Double Check (Bronze) - Deliver a check by two pieces at the same time.
En Passant (Bronze) - Perform an En Passant during any full game.
Epaulette Mate (Silver) - Deliver checkmate where the king is blocked on both sides by his own rooks.
Grandmaster (Gold) - Achieve an ELO of 2500 or a Grandmaster Pure Chess rating.
O-O-O (Bronze) - Perform a castling move on the queenside during any full game.
Piece Collector (Bronze) - Capture 100 pieces.
Problem Wizard (Silver) - Solve 100 mate problems.
Promotion (Bronze) - Advance a pawn to the eighth rank in an offline game.
Pure Correspondence (Bronze) - Win a game of Play By Mail.
Tournament King (Silver) - Complete Tournament mode on all three difficulties.