Surprisingly enough, Boss Max Brass isn't that difficult of a character to overcome (even at higher levels of difficulty). In all truthfulness, he's not even as good at Min Min, Ribbon Girl and Ninjara (the best three Fighters in the entire game). However, it isn't even necessary to be one of those three characters to defeat him - though it does help - as any fighter found in the game can do that very job.
The best way to defeat Boss Max Brass is by taking things slow. Don't Rush him with attacks that he will easily block and take advantage of. Try getting the hang of his style first by avoiding a few of his throws, and then unleash a few of your own once you get use to his habits and have created an opening after a given dodge or two. Always make sure to use a character you have a good handle on - including their given special Abilities - as well as a selection of Arms that you are an ace at using. If you do these simple things, any player using any character can defeat the current champion of the Arms League.