Here is the full list of all 19 Undying Lantern achievements.
Cinder Hall puzzle solved
Zealous Tiger weakened
Finished the first level
Cottage puzzle solved
Shapeshifter weakened
Finished the second level
Castle puzzle solved
Finished the third level
Cannon Broken
Captain weakened
Finished the fourth level
Garden puzzle solved.
? weakened
Finished the fifth level
Final puzzle solved
Beat the game in Haunter Mode