But does Bullseye have any feats like that? Let's put it like this. Bullseye being good with improvised weapons has nothing to do with marksmanship. Rorschach is good with improvised weapons too that doesn't make him a better fighter than Ozymandias, the Comedian, or Owlman.
It would be a good fight, I'll give you that. But Batman would have taken him down the moment he met him, and he wouldn't have gotten out. Gotham city was more corrupted than Hell's Kitchen before either character tried to clean it up and he managed to imprison most of the corrupt police officers in the GCPD and his actions caused Commissioner Loeb to resign.