I'll just point this out. Batman is a vigilante. He has never really worked within the boundaries of the law. Whether the GCPD gives him any leeway is their own damn initiative - you know that Bruce would continue his mission without support without even shaking his head. There is NOTHING here that is in anyway contrary to his modus operandi. Striking a detective and taking her gun? To protect his own life, I don't see why the hell not.
Could he have diffused the situation? Sure. But ask yourself this: is it in any way correct judgment to SHOOT when someone does not obey your order? I think that except for extreme cases we would all find such judgment poor. Especially Batman, who has a record of NOT killing people or police officers.
Sorry, but your glorification of the police lacks the analysis that should be applied any time to a lawfully appointed, government controlled, and taxpayer funded organization.