Jack Johnson had to fear for his life before, during and between fights. He was truly hated and yet he persevered in the most defiant fashion imaginable at the time. Not sure it's possible to be braver
Sam Langford fought anybody from any weight. He fought top tier HWs when he was half-blinded and washed up. Bob Fitzsimmons was a MW who fought two of the best HWs in the world at almost 40 within a few months (and he stopped them quickly). He feared nobody and I'm sure he wouldn't fear modern giants either.
The Hagler fight alone convinces me that Mugabi was one of the bravest of all time. Frank Fletcher and James Green were pretty gutsy themselves.
I see Duran, Mugabi, Bert Cooper and James Green mentioned. Tough but each one had at least one fight in which they quit.
What fight did Mugabi quit in? As for Cooper, he proved what a brave guy he was after the Foreman fight.