In real life, ancient soldiers faced angry war elephants, and they learned how to fight them -- namely by getting out of the way and then throwing javelins for the eyes as they charged past.In real life, the guy attacking a rhino with a sword gets turned into paste. In D&D, it's just another day at the job.
That's the kind of thing I'd like to see more of in the game -- using the right tactics to defeat a ferocious beast.
If you prefer mythical inspiration, then have your heroic fighter wait in a ditch for the dragon to slither over him. Then he can plunge his sword into the beast's soft underbelly.
That's the kind of "mundane" answer I'd prefer to see, rather than simply giving the hero more hit dice and bigger bonuses, so he can stand toe to toe with a grizzly bear.