Complete the Arcade mode. You will unlock the classic themes for both characters in your team.
Win your first three matches, and have at least one perfect finish.
Hold down a punch or kick button at the end of a round to change your character's win pose.
After unlocking the classic themes for every character, including Shin Akuma and Pyron, hold the X button and hit Start while selecting arcade mode. You'll now be able to play through aracde mode using the classic bgms for all of the characters in the game.
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.
Also, 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).