I mean Batman is just a really rich guy with a fancy suit. Technically a person with sophisticated martial arts skills, highly technical gadgets and weaponry, a research and development team that makes him badass accessories and vehicles, billions of dollars, and just a shit ton of skill could essentially be a real life Batman?
Obviously this batman would have to use guns, or some variant thereof, but besides that, I see no reason why someone like Batman couldn't exist. Most of the tech in Batman, or at least similar technology already exists as Military weapons projects, it just isn't available in the mainstream, or to the wider public.
Batman seems to be a comic-book superhero that could actually potentially exist in real life.