Extra Stage Boss Songs in Normal Play
You have to be in Game mode to unlock the 'Boss Songs' used in Extra stage and on your last stage clear a song on Expert with a AA grade or higher to play the Extra stage. When you clear Extra stage you then play Encore Extra stage where you have to complete the Chaos song without making a mistake. Anything other than a 'Perfect' or 'Great' and it will immediately end. If you clear the Chaos song you can then purchase it in the shop.

Unlock MAX 300 (Super-Max-Me Mix):
Clear it on Extra Stage on Easy Song Sort with an A or higher

Unlock Healing-D-Vision:
With an A or higher clear it on Extra Stage on Medium Song Sort

Unlock Fascination MaxX:
With an A or higher clear it on Extra Stage on Hard Song Sort

Unlock Fascination-Eternal Love Mix:
With an A or higher clear it on Extra Stage on ALL Music Song Sort.

Unlock Chaos:
Clear the Encore Extra Stage with a full-combo