Here is the full list of all 20 Realm of the Ghost King achievements.
Find a secret level
Beat the game in Tourism Mode
Play Endless Mode. It does end.
Get through The Graveyard
Get through The Catacombs
Defeat the Ghost King
Defeat the Ghost King three times
Defeat four enemies at the same time
Destroy the Moai in the Snow Cliffs
Defeat the Void Queen
Get to The Depths
Unlock every alternate skin
Unlock all nine original characters
Unlock the three newest characters
Defeat the Ghost King as the Ghost King
Score 100 or more points in a game
Beat the game with GhOsTY (only active in January)
Get a score of 40 or more in an Endless game