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