To fight the secret bosses in USF4, you need to not lose a round and meet a few special requirements along the way. If you set battles to 1 round instead of 3 rounds, to fight Oni you'll need to get (at least):
- 5 first attacks
- 3 ultra or super finishes including on Seth, the final boss (otherwise, you fight Gouken)
- 1 perfect round
and never lose a round. If you think you're going to lose, hit start on a second controller (or your keyboard, if you're using a controller) - this will set off a local challenge and then return you to arcade mode afterwards without losing your streak!
Zangief's lariat (press all three punches or kicks at the same time) is a simple way to cheese most of the AI opponents, but you might have to play legitimately instead.