Is Hamlet a noble hero?
If by a noble hero, we mean a warrior hero in the mold of Greek and Roman epics, then, no, Hamlet is not that kind of hero. Laertes fulfills that role, rushing heedlessly to fulfill the warrior code that demands a son avenge his father's death without a second thought. Hamlet, however, may stand tall as the first modern hero.
Hamlet has long been noted by critics for his interiority, meaning that he reflects on and thinks long and hard about the implications of his father's death and about avenging it. He asks thoughtful and serious questions in his long soliloquies. He wonders if the ghost of his father really is his father or a trick played on him by the devil. He wishes he didn't have to kill his uncle. He has self-doubts, just as a modern person would. He toys with the idea of suicide in a world that seems to him to be wholly corrupt. He takes the time to try to confirm that the ghost is telling the truth rather than just mercilessly slaughtering a man who might be innocent. This is a modern, rather than "heroic" or "noble" mindset.
Critics have often condemned Hamlet as "indecisive." Why doesn't he simply kill Claudius and be done with it? But as Rene Girard notes in his book A Theater of Envy, Hamlet behaves reasonably and even heroically in rejecting a culture of mindless revenge based on the "warrior" or "noble" hero. As Girard puts it:
Should our enormous critical literature on Hamlet someday fall into the hands of people otherwise ignorant of our mores, they could not fail to conclude that our academic tribe must have been a savage breed, indeed. After four centuries of controversies, Hamlet’s temporary reluctance to commit murder still looks so outlandish to us that more and more books are being written in an unsuccessful effort to solve the mystery. The only way to account for this curious body of literature is to suppose that back in the 20th century no more was needed than the request of some ghost, and the average professor of literature would massacre his entire household without batting an eyelash.
We can admire Hamlet for being a new kind of hero.