Here is the full list of all 20 KNIGHTS achievements. It takes around 6-8 hours to unlock all of the achievements on Windows.
Clear the KING Level Pack
Clear 5 Daily Levels (Total, Not on the Same Day)
Clear 10 Daily Levels (Total, Not on the Same Day)
Clear 25 Daily Levels (Total, Not on the Same Day)
Obtain All Achievements
Move 4000 Pieces
Clear the QUEEN Level Pack
Clear A Daily Level
Clear a 5x5 Level
Clear Level KING-B1 Without Touching Any Yellow Pieces (For Clarification, the KING Level Pack is the Last One)
Unlock Daily Levels
Clear a 5x4 Level
Clear the BISHOP Level Pack
Clear the ROOK Level Pack
Move 400 Pieces
Clear a 4x4 Level
Clear a 4x3 Level
Clear the PAWN Level Pack
Move 40 Pieces
Clear a 3x3 Level