Here is the full list of all 16 King 'n Knight achievements.
Complete the graveyard.
Complete the magic forest.
Complete the orc cave.
Complete the haunted city.
Complete the cursed swamp.
Complete the ice mountain.
Complete the swarming tunnel.
Complete the dark sea.
Complete the burning land.
Complete the black castle part 1.
Complete the black castle part 2.
Kill the king.
Complete the game solo.
Complete the game in co-op.
Obtain all the achievements
Complete a level entirely without taking damage.