To unlock the Endless, Survival, and Combo Challenge modes for Advanced Mode, unlock and purchase all songs from the shop. This will be indicated by the "New items in stock" message when you purchase the last unpurchased song. The modes will then be available for purchase.
To unlock Concent Be-fU as a dancing character, clear all missions in Areas A-J of Hyper Master Mode (single). Concent Be-fU can then be purchased in the Shop for 20,000 points.
To unlock Double Mode for Hyper Master Mode, complete all missions in Areas A-J in Hyper Master Mode (Single).
To unlock the hidden Area K in Hyper Master Mode, complete all missions in Areas A-J and clear all Area Boss Missions.