Complete Chronicle mode, then finish the indicated task to unlock the corresponding Boss!

Boss	How to unlock
Alpha-152	Complete Mission 19 in Tag Challenge mode.
Genra	Complete Mission 18 in Tag Challenge mode.
Kasumi Alpha	Complete Tag Challenge 16.
Raidou	Complete Tag Challenge 20.
Shiden	Complete Tag Challenge 20. Select by holding L+X and Press A on Random.
Tengu	Complete Mission 17 in Tag Challenge mode.