I think Joshnorm has the best method, but I want to get a little more detailed.
First off the achievement description says that you need 5 perfect rounds in arcade mode. What it doesn't say is that this isn't cumulative. Meaning all 5 perfects MUST be gained in a single arcade playthrough.
Start up Arcade mode with the following settings:
One thing worth noting is that the enemy AI gets more difficult the further you progress so it is wise to get this before your 3rd or 4th opponent. If you don't you're probably better off restarting.
As Josh has outlined M. Bison makes this task a breeze. For some reason the enemy AI cannot block Psycho Crusher. Just be sure to alternate the speed when the enemy is at low life.
Another alternative is to use Sagat and spam Tiger shot. (quarter circle forward + Punch) alternate with the Kick variant for maximum effectiveness.
It can be frustrating to have the enemy ruin your perfect when they are a thread of HP away from death, but just keep at it and the achievement is yours.