Unlockable: Pyron
Beat the game on Normal difficulty.
Unlockable: Shin Akuma
Defeat Shin Akuma in Arcade mode (any difficulty). To make Shin Akuma appear in arcade mode, you must win every round, get at least 3 perfect rounds (one perfect within the first three fights) and have at least one super combo finish.
Alternatively, you can simply complete the game's Arcade mode with every character in the game (completing it once counts as completing it for both characters in your team).
Unlockable: Classic Character Themes
Complete the Arcade mode. You will unlock the classic themes for both characters in your team.
