To unlock the following End Game options like New Game+, Jukebox, Invincibility and more complete the following tasks.

Unlockable	How to unlock
Art Gallery	Beat the game once.
Invincibility	Locate every 100 Stray Beads.
Jukebox	Beat the game.
Kamic Returner	Finish the game once.
Kamic Transfomer 1	Finish the game once.
Kamic Transfomer 2	Finish the game once.
Kamic Transfomer 3	S-Rating for "Deaths".
Kamic Transfomer 4	S-Rating for "Enemies Defeated".
Kamic Transfomer 5	S-Rating for "Money Gained".
Kamic Transfomer 6	S-Rating for "Demon Fangs Found".
Kamic Transfomer 7	S-Rating for "Praise Earned".
Kamic Transfomer 8	S-Rating for "Praise Earned".
Kamic Transfomer 9	S-Rating for "Praise Earned".
New Game+	Beat the Game one time.
Secret Theatre	More than 31 hours of play time.
Stray Bead	Finish the game once.