A tragedy is a type of drama that usually involves human suffering. Often, the characters who endure suffering are both admirable and flawed. It would not be tragic if a completely evil, heartless character underwent some horrible event. A tragic character is one who has some decent qualities. The audience has sympathy for the tragic character (they would find it difficult to have sympathy for a character with no redeeming qualities) and the evocation of this sympathy is called pathos. The audience feels sympathy and/or identifies with the tragic character. Notice the root 'path' in pathos and sympathy.
So, for Hamlet to be a tragic character, or hero, we must find something sympathetic or identifiable about him. This isn't hard to do. His father was murdered by his uncle and his mother quickly married that uncle. At least, we can sympathize with his loss.
We might also admire Hamlet for his emotional depths and philosophical intelligence. Hamlet is one of the more complicated figures in tragic drama because he is such a profound thinker, also something to be admired. Ironically, Hamlet's tendency to think so deeply about things is not only a quality we admire; some critics think it is also his tragic flaw. It is his constant philosophizing that delays his vengeance and also leads him to consider suicide. Part of the tragedy is deeply affected Hamlet is.
Hamlet's drawn out method of madness, en route to avenging his father's murder, causes him to offend Ophelia which then leads to her own death. In his treatment of Ophelia, I would say he is less than heroic; more of a tragic figure.
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Thanks for the perfect and the extensive answer, and dun worry my teacher is an old school he isn't even what is the internet ;)