Destiny mode is a secret/debug mode developed during v11-v12, which was formerly supposed to be the "final ARC" of the story. It was scrapped near the main mode's completion, with it's replacement being the Blockquiem of Destruction ARC (The actual final ARC).
The mode is now repurposed to be the hardest difficulty in the game, and can be unlocked by inputting the Konami Code (^ ^ v v < > < > B A Start).
EDIT: Incase you missed it, it's HARD AS forget to beat.