@DoubleI would say that by that definition Batman is an anti-hero. He doesn't always do things "by the book".
Anarchy's goal was to free people from theft, coercion, assault, slavery, murder, etc. especially when it was done by an organized group.
That is what the government was, at least in his view, which is why he began targeting government installations and exposing their crimes. When he was attacked by their soldiers, the Justice League, he fought back by joining with criminals and, in the process, was able to lessen the severity of their crimes. Sure, joining them wasn't right, but if he didn't he would be in Belle Reve, so he fought back.
His goal was to free people and save them from criminals, that just happened to include the government. He still protects people, only now it's as private security. He did dark things, helping criminals with minor crimes and counter-attacking the "heroes", but he did it to work towards his goal, and only as much as was needed to complete it.