To be able to fight Akuma in arcade mode there are three things required:
1. Get 1 perfect in one of the 4 fights
2. You have to win the 4 fights under 3 minutes (exact minimum time not confirmed)
3. You can't use a continue
If you follow my instructions, you'll get to Akuma in less than 1 minute!
To make this easier, go to game settings and change the CPU difficulty to Easy and set it to 1 round.
Then, go to Arcade mode and choose Law as your character.
move will destroy the AI and will almost definitely get you a perfect.
As long as you get a perfect in one of the first 4 fights, you'll face Akuma after Heihachi because of how fast we're doing this :)
When facing Akuma, just use the same tactic and the achievement will pop as soon as you win that fight.
Here's a video of how I did, the achievement didn't unlock on screen because I already had it.