It was very hard to me to get this achievemenet, to beat the final boss (every other opponent was so easy...). I've tried many times, failure every time. It was even so hard to win at least one round. I was trying hard, using different characters, power-ups, etc.
And to be honest, I've found very easy way, thanks to player PANIC ATTACK 10 and his post on xbox360achievements.org. You have to choose Shadow X. At the beggining attack with his underground attack (you have to jump, your character goes underground and gets close to the opponent) and after you hit just have to keep in close combat - move forward you opponent and just kick and punch him. You don't have to make the final punch/kick, just make sure you keep in close combat and do some damage every time during you powerup charging. But you have to be fast, timing is very important - always try attack with this only one powerup and then get close to your opponent, dont's let him hit you with his power strikes.
Don't bother with dodging, just attack. When you are underground he should not be able to hit you with any of his attakcs. If you see him charging you can try to shoot him to stop his attack but if you are fast enough you should be able to get close to him before he attacks.
With this method I was able to beat the final boss on second try. It is quite exhausting but really easy after some practice with timing.