"Every reason?" I don't know. If you're going to apply the idea that she has common knowledge of Batman to the degree that she knows he carries weapons, it makes sense to assume that she knows other things about him. Such as him working with the cops most of the time, never using lethal force, etc.
The argument that the shoot to kill is justified would hold if he were an unknown commodity. But it's Batman. And the Penguin. So there's some prior knowledge to be factored in and it's not a case of jumping in blindly.