This method works in all three modes. It is not 100% fool proof but it should work a majority of the time from my experience.
Pick Mature as your first character. She is the second from the right in the bottom row. The other characters hopefully won't matter as Mature will let you win without needing their help. I used King as my second character since their jump kick

and standing kick

both seemed to work well.
The key is really to last all three rounds in every fight as Mature since that will give you a Straight Bonus which is worth more than Perfect bonuses.
The only attack you will be using with Mature is the

button. You will not duck, you will not jump, only walk backwards and forward and press

. Try to learn the distance this kick will connect from and stay at that distance. Being aggressive is good so don't wait for your enemy to attack. Cornering an enemy is great if you can do and it often works to use this kick on enemies just as they stand up since it will knock them down again if you time it properly. Repeat when they try to stand up again.
Demonstration of the method but not a full playthrough:
This solution was originally posted by someone else on TA but has for some reason been deleted.