/ his fighting style becomes progressively more lethal and he learns more offensive focused martial arts throughout it

/ he actually doesn't want to kill again so the fact that his fighting ring slowly ramps up the stakes until he's forced to kill / cause lethal or fatal harm to his opponents in a fight for survival

By the time he's invited to the tournament he's far too used to having to take another's life

/ I was thinking he has a primary focus on boxing / kickboxing
a base level of defensive martial arts like aikido or BJJ

it isn't exactly friendly, a bunch'f criminals crawlin about, hiding 'round the place.

most'f the time lookin for someone to mug fer quick cash——

I think I'd be more concerned if kids were in this part'f town—— fuck even a pretty lady like you 'round here has me concerned