New Single Player Modes
Caravan mode allows you to play specific stages.
Boss Attack allows you to fight all of the game's bosses.

Unlockable         How to Unlock
Caravan            Complete Arcade mode once
Boss Attack        Complete Arcade mode once

Stage Omega & Stage Alpha
     To unlock these stages, simply clear each stage with an A rank or
better for Stage Omega, or a C rank or worse for Stage Alpha. The best
way  to get a good ranking is to get all quickens as fast as possible,
then  make huge combos. The best way to get a bad ranking is to not do
anything at all. Simply dodge the enemies and bullets, then defeat the
boss.  It's  still  alright  to  get  quickens,  but only quickens, no
combos.

Unlockable         How to Unlock
Stage Omega        Get an A rank or better on each stage in arcade mode.
Stage Alpha        Get a C rank or worse on each stage in arcade mode.