Batman invests all of his time, money, and energy into fighting crime, but it is a never ending battle. Eventually it will kill him, like it did Hamlet. The question is when. The real enemy is the system he protects and, like Hamlet, he can't see it. He just keeps on fighting. Both characters are noble in the classic sense, but neither are heroes either. They are fighting irrelevant ghosts. For Batman to truly win and avenge his parents death he must fight homelessness, poverty, debt, and bad education (but he can still chill with jewel theives), and work to end the grip that capitalism has on Gotham. It was poverty that created corruption and crime in Gotham and only the end of poverty will bring peace to Bruce Wayne/Batman.
Unfortunately for Bruce and Hamlet they will never attain their goals. Batman will never show Gotham what it can be until he realizes what it shouldn't be. Justice will only come through systemic change in Gotham. That Batman doesn't realize this is as tragic as Hamlet's spiral downward throughout Shakespeare's work. Batman is doomed to never quite comprehend what his first love understood about justice; it is actually found in harmony as opposed to revenge.
None of this should diminish the truth that Batman (and Hamlet) are bad ass, human characters who are fighting very real personal battles on the inside and out. I just think that Bob Kane may have been a Red trying to communicate the futility of consumption capitalism as the basis for a fulfilling life by depicting the never ending battles that Batman must face.
UPDATED December 4th, 2012:
Regarding a discussion of whether Batman is in fact just a rich, capitalist, fascist who beats up on the poor of Gotham: The idea of superheroes in general can be seen as anti-democratic (who watches the watchmen?). It is the (literal) concentration of power in an individual who controls the fate of cities and worlds. Only the truly lucky few magical-alien-rich-science-wizards share in the power in these worlds. I don't think Batman is unique in this regard. I think that this notion of concentrated power is only magnified in Batman, perhaps, because he has no superpowers (only money, skills, and serious vehicles) which makes him seem closer to reality. (Christopher) Nolan's films, which keep the magical and supernatural at a safe distance, also put these stories of an individual wielding too much power in the realm of the "real" and therefore politically relevant in terms of his actions. Because the films do a good job of portraying a "realistic" Batman, we begin to analyze the obvious problems that such a character poses for Leftist activists and thinkers. Many of these issues are discussed in Frank Miller's "The Dark Knight Returns" I just think it is also important to think about this in the context of all the beloved and deeply violent characters out there (superman, spiderman, x men - who carry a great anti-hate message -, knights, terminators, the lion king…). Critical thought and media literacy are of vital importance in order to be able to escape into lalaland, even masked vigilante counter-revolutionary lalaland.