Haven't followed comics super seriously in a while but: mainly he fights other supervillains and to be honest they're actually genuinely trying to address this question.

One of the best runs on him in the modern era was the court of owls storyarc, and I think the current line of movies are trying to set it up based on vague info from the promotional material. The short version is (with a bit of interpretation): Batman takes on the old wealth eyes wide shut style gothamites and finds out that his whole run as Batman has been a sort of amusing distraction he has been allowed to engage in because he's never actually challenged the real power and reason for Gotham's suffering. They don't really have him change significantly as a character afterward but they also recently had him lose a ton of wealth so there is a genuine effort to try and square the circle and have Batman still exist and be relevant in a world where its becoming increasingly harder to ignore that the real villain and source of Gotham's plight is Bruce Wayne and his desire to keep living in his adult wonderland where he can play with scifi toys beating up the poor and mentally ill every night rather then address the material conditions that make Gotham the way it is.

A lot of uncovering conspiracies and fighting assassins. Modern Batman is more of "privatized CIA" than "rogue vigilante" these days.

He hasn't fought petty crime since like, his 3rd issue. He lives in a world of killer clowns (also known as clowns) mad scientists, plant monsters, crocodile men, aliens, and undead ancient warriors. Batman is fascistic IF you try to be grim and gritty with him. If you do brave and the bold or Morrison then it is great

Punch bad guy

There's an upcoming movie where he's gonna be more of a detective or whatever so there's that.