Spoiler contains the character required along with how to unlock them.
The Haunted Chest is unlocked by defeating Mega Satan using
*** Spoiler - click to reveal ***Tainted Lost, who like all tainted characters is unlocked by using a Red Key or a Cracked Red Key in the left hallway of Home while playing The Lost.
Due to the nature of this character, this can be an incredibly difficult achievement to earn, and relies on both skill and lucky builds. Don't get discouraged, as this will likely take you many runs before you get it.