Play Game mode and reach a Boss stage, then get an A rank or higher for the song to unlock in for purchase in the shop.
Completing missions faster
Go to the "Options" menu. Set the game to an option you need to have activated to complete a mission while doing other missions, for example, "Get Bs on all songs" or "Complete 10 songs".
Finish Healing-D-Vision
Finish on Extra Stage on Medium Song Sort with an A or higher.
Finish MAX 300
Finish on Extra Stage on Easy Song Sort with an A or higher.
PizzaBox World
Get all VIP cards to unlock the secret world 'PizzaBox'.
Unlock Chaos
Finish the Encore Extra Stage with a full-combo.
Unlock Fascination Eternal Love Mix
Finish on Extra Stage on All Music Song Sort with an A or higher.
Unlock Fascination MaxX
Finish on Extra Stage on Hard Song Sort with an A or higher.