Well the Arkham games do a great job of an overworked Batman.I think Batman in general works better as a concept & story when GOTHAM itself is the 'villain'. What I mean by that is, there's CONSTANT crime & corruption that he's always battling against, but never a sign that it's going to get better. It's that struggle against the unyielding enemy of human nature, knowing that it's unwinnable, but continuing to fight against it every night, that makes Batman who he is to me.
In my mind, each of his Rogue's Gallery members is always either in the planning stages of something, or in the midst of it. Penguin is running some underworld thing, Falcone has something going on at the docks, Catwoman is stealing something, & the Joker is just sowing anarchy. That's on top of Gotham just being Gotham. Batman's aware of all of it, but has to prioritize his efforts.
Other than Batman Begins, I'm not sure a film about him has really shown that, & I can't really say how to do it, but I guess I'm just saying that Batman is Batman to me when he almost has TOO MUCH on his plate.
AmenWell the Arkham games do a great job of an overworked Batman.
Asylum has Batman having to deal with Arkham Asylum and a good deal of his rouges gallery.
City turns it up with the entire city turning against him (citizens basically left the section of Gotham you are in).
And Knight turns it up to eleven with Batman mentally struggling against Joker and physically against his gallery and a new villain. Batman arguably gets overwhelmed and “loses” in Knight.