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