Okay so ive done the boxing tournaments basically every time i go through the game, some times being much harder then others.
This time was by far the easiest time ever, without having a character that used any sort of unarmed skill whatsoever. In fact, i won the entire tournament - beating every single opponent without swinging a single punch or attacking once.
So this is the first playthrough i actually took the "jinxed" trait, giving you more critical failures as well as everyone else.
When i first started the fights, i would go in and try to punch and eventually (usually pretty quick) i would get a critical failure which resulted in you losing the next turn. If that happens, you automatically lose by knockout (in fact any time you're caused to miss a turn it will become a loss - the same goes for the enemy).
So after realizing that i wasnt gonna win by fighting, i went into the tournament and literally just skipped my turn every time. Within 1-5 turns, the guys should critically miss, causing them to miss their next turn - giving you a win. I went through every opponent without healing once, with a max hp of 72 at the time and didnt swing a single punch - i am now the boxing champ.
I found in another playthrough as well (where i didnt use unarmed either, but had a decent skill from the various places it can get raised in game), i was getting outclassed by the boxers and there was no way i could beat them shot for shot. So what i did was aim every shot at the groin. Groin shots have really high chances of knocking them down, as well as a high chance of making them miss their next turn (which results in an automatic win). I won the tournament once by nut shotting every guy until they slumped out of the fight.