Unless you’re talking about actual superheroes with real superpowers, not very. Firearms aren’t actually the sticking point, ironically.
If you’ve ever played games with well developed stealth systems, you should have some basic ideas for how a sufficiently trained individual can neutralize armed opponents. Actually, while we’re talking about it, the Arkham games do a pretty good job of this when we’re talking about a Batman style superhero.
We’ve talked about how children can’t go toe to toe with adults before, and again, unless your Robin stand-in is more in the 16-20 range, or has actual superpowers, they’re just not going to be able to take on adults in hand to hand, no matter how good their training is.
The real problem is, this isn’t sustainable behavior. Mark Millar’s Kickass does a pretty good job of showing what will happen when a character like that screws up in a fight. At least the comic does, I still haven’t gotten around to the film.
But, of all things, the Ben Affleck Daredevil film pays lip service to the consequences for an (effectively) unpowered character doing this without screwing up and getting mauled. If you haven’t seen it, there are a couple shots early on in the film showing that he is downing massive cocktails of painkillers on a daily basis just to remain functional.
Here’s the thing, even if your character fights effectively, they’re going to physically deteriorate at a phenomenal rate. This is why boxers and other professional fighters have careers that only last at most a decade. Martial artists who don’t participate in competition last longer, but people who are engaged in real world combat, are looking at a couple years before their bodies are complete wrecks. This isn’t a skill issue, this is just that they’re pushing their body past the breaking point every night, and it quickly catches up with them.
For powered characters, who have faster healing or increased resistance to damage this is obviously, less of an issue. Also characters like the Punisher or The Shadow that rely more on weapons to dispose of criminals will be mostly unaffected by this. (Though, now that I think about it, The Shadow probably does have increase healing from his training, so that example just undermined itself.)
Looking at Garth Ennis’ Welcome Back Frank isn’t a bad place to look at someone balancing comic book sensibilities with the consequences of failure for The Punisher, and characters like him.