You just have to get more than 60,000 points in "HI SCORE MODE" and then lose so you can enter your initials. The achievement will then pop.
I used the guides that were already posted for obtaining the 60,000 points. A good thing to know is that if you are rewarded a perfect during a round, you get an extra 30,000 points. If you are able to get two perfects in a row against the female fighter, you can knock all of the hi score achievements out in about 2 minutes.