Depends on what version of Batman, the strongest version of Batman has beaten super aliens capable of defeating the entire Justice League (besides Batman of course), but at certain stages he's been heavily inhibited, such as right after his TV show came out and he lost all darkness and became far to...

I believe Haku was a boy, even after reading all of your information. While I understand where you're coming from rather well actually, I just don't think Kishimoto would be that deceptively brilliant, when the rest of the series is so simply straight forward, no offense meant but it sounded like yo...