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
Obtain All Achievements
Clear 25 Daily Levels (Total, Not on the Same Day)
Clear Level KING-B1 Without Touching Any Yellow Pieces (For Clarification, the KING Level Pack is the Last One)
Move 4000 Pieces
Clear a 5x5 Level
Clear 10 Daily Levels (Total, Not on the Same Day)
Clear 5 Daily Levels (Total, Not on the Same Day)
Clear A Daily Level
Clear the QUEEN Level Pack
Unlock Daily Levels
Clear a 5x4 Level
Clear the BISHOP Level Pack
Clear a 4x4 Level
Clear the ROOK Level Pack
Move 400 Pieces
Clear a 4x3 Level
Clear the PAWN Level Pack
Move 40 Pieces
Clear a 3x3 Level