Here is the full list of all 38 Chess Ultra achievements.
Complete all the chess challenges
Complete 50% of the chess challenges
Capture 100 pieces
Promote a pawn to a Rook, Bishop, or Knight instead of a Queen
Using a Knight simultaneously attack the enemy King and Queen
Beat an opponent with an Elo rating more than 75 higher than yours
Beat an opponent with an Elo rating more than 150 higher than yours
Beat the computer on Grandmaster difficulty
Deliver a check by two pieces at the same time
Complete all the tutorials
Perform an en passant capture
Advance a pawn to the eighth rank
Castle queenside
Castle kingside
Create a random online game
Develop a White King Bishop to b5
Place a White Knight on e6
Issue an online challenge to a friend
Deliver checkmate by two crisscrossing Bishops, with the King's escape blocked by friendly pieces
Draw a game by stalemate
Sacrifice the Queen then go on to win the game
Win a game in four moves
Deliver checkmate where the King is blocked on both sides by his own Rooks
Deliver checkmate by a Rook or Queen along a back rank, with the King's escape blocked by friendly pieces
Put an opponent in check
Win a game in three moves
Beat an opponent with an Elo rating higher than yours
Pin a piece against your opponent's King
Manoeuvre a pair of Rooks onto your opponent’s second rank
Have two pawns of the same colour on the same file
Make a capture or exchange
Win a game
Play a game using the Fischer timer
Stack two Rooks one behind another in the same file with the Queen at the rear
Win 20 tournaments
Win 5 tournaments
Win a tournament
Win a 32 player tournament