Hamlet has a hard time being heroic. In fact, he has a hard time making up his mind about anything. It has been said by some critics that Hamlet is the first "modern" hero because he's so conflicted. In your estimate, is Hamlet a hero?

Whether Hamlet should be considered a "hero" is a matter of how you define the term "hero." In literary criticism, the term originates in Aristotle's Poetics. Aristotle is trying to define what makes an ideal protagonist for a tragedy. The hero, according to Aristotle, must be a figure who is greater and more noble than the average person. We must sympathize with them but also recognize that they have a character flaw that leads to their own downfall. The element of sympathy is required to evoke fear and pity at the character's reversal of fortune.
As Hamlet is a prince, braver and more intelligent than most, who suffers a reversal of fortune and with whom we sympathize, he fits the general profile of a legitimate tragic hero. There is nothing in the Aristotelian definition that requires immediate and unconflicted action. In fact, a genuine tragic hero is often faced with genuine and sometimes unsolvable dilemmas. Hamlet's wanting to be sure that Claudius is guilty before he kills him seems like good moral judgement rather than a sign of weakness. His treatment of Ophelia is more morally problematic, displaying a certain ruthless quality.