Here is the full list of all 19 Curse of the Crescent Isle DX achievements. It takes around 3-4 hours to unlock all of the achievements on Windows.
Complete Speed Run Mode
Collect all 27 coins in the game
Complete the game with no coins
Complete the Boss Rush Mode
Complete the game as the Queen
Find one of the special messages in the password screen
Complete the game as the King
Defeat Aranomanom
Hit the third boss three times on its way up
Break one of those big rocks
Let a Carfee fall in the water
Defeat Naja Naja
Talk to the statue in the town
Defeat Grondor of the Forgotten Mine
Take damage by staying underwater too long
Jump off an enemy while grabbing him
Complete a stage without taking damage
Complete a stage in co-op
"Accidentally" kill an enemy