If you are talking about fighting as it is, with no rules, well then, baby, you’d better train every part of your body.
They say: Don’t skip leg day.
I say: Don’t skip any day!
Legs, Arms, Abs, Back, Core, the list goes on. Training is more than muscles, it is about mindset, coordination, strength, endurance, it has a lot of facets.
And this is not only about training for fighting, of course. It applies to any kind of training and is a good reminder of diversity in the gym (or wherever you may train)