Capcom Fighting Collection

First make sure you are playing the Japanese Version. The USA version is known to have very difficult AI.

Change game options to the following :

Game Difficulty : 0
Max Rounds : 2(First to 1)
Coin Mode : Free Play
Akuma/Gouki : Easy Select
Normal Mirror Matches : Allowed

Choose your best fighter and make sure to save before the start of each match.
The requirements to fight against Akuma(Gouki) is to reach M Bison(Vega) without losing a single round.

In the arcade you had to do the above and get four "perfects." , but it has been confirmed by Cinderkin that you only need to get to M Bison with no rounds lost.

I kept using fireballs to win my fights quickly (41236 RB)

You can keep making a quicksave before each fight and if you take any damage load your save.

When you are supposed to fight against M Bison(Vega) Gouki will apear which will unlock the Achievement.