Here is the full list of all 39 Chess Ultra trophies - there are 26 bronze, 7 silver, 5 gold and 1 platinum.
Win a game in three moves
Issue an online challenge to a friend
Complete all the tutorials
Perform an en passant capture
Complete all the chess challenges
Complete 50% of the chess challenges
Capture 100 pieces
Castle queenside
Sacrifice the Queen then go on to win the game
Advance a pawn to the eighth rank
Promote a pawn to a Rook, Bishop, or Knight instead of a Queen
Castle kingside
Create a random online game
Play a game using the Fischer timer
Develop a White King Bishop to b5
Pin a piece against your opponent's King
Have two pawns of the same colour on the same file
Beat an opponent with an Elo rating more than 150 higher than yours
Beat an opponent with an Elo rating higher than yours
Beat an opponent with an Elo rating more than 75 higher than yours
Win a game
Beat the computer on Grandmaster difficulty
Deliver a check by two pieces at the same time
Place a White Knight on e6
Using a Knight simultaneously attack the enemy King and Queen
Put an opponent in check
Make a capture or exchange
Unlock all other Trophies
Stack two Rooks one behind another in the same file with the Queen at the rear
Deliver checkmate by a Rook or Queen along a back rank, with the King's escape blocked by friendly pieces
Deliver checkmate where the King is blocked on both sides by his own Rooks
Win a game in four moves
Win a tournament
Win 5 tournaments
Maneuver a pair of Rooks onto your opponent’s second rank
Draw a game by stalemate
Deliver checkmate by two crisscrossing Bishops, with the King's escape blocked by friendly pieces
Win a 32 player tournament
Win 20 tournaments