Without all the events and devious plots, Hamlet himself is tragic, is he not? Hamlet himself, as Harold Bloom writes, "appears too immense a consciousness for Hamlet the play." So, to write about Hamlet, you may wish to demonstrate how Hamlet transcends the consciousness of the play Hamlet. Rather, he is a major tragic character of the theatre of the world such as Faust or Ulysses. For, no other single character in Shakespeare's plays matches what Bloom calls "infinite reverberations."
Focus on Hamlet as the initiator of the tragedy within himself and without. His soliloquies are all that initiate action. Nothing happens without the soliloquies as they are what propel events.
If I were writing this essay, I would start by including Aristotle's definition of a tragic hero: being a great (noteworthy, decent) man, dying, with a tragic flaw that brings about his death.
I would describe why it is so hard for Hamlet to avenge his father's death: I actually find him a sympathetic character. He wants to do as the ghost asks, but is afraid that if the ghost is not "honest" (or is sent by the "powers of darkness") that he might be tricked into forfeiting his soul. Remember that the Elizabethans (of which Shakespeare was one) believed that it was a moral sin to kill a king, and this play raises the question as to whether killing was permitted if a tyrant was sitting on the throne.
Hamlet also wants to kill Claudius when sins rest heavily upon him. He does not kill him as he is praying for then he would be sinless, and when he does act, believing Claudius to be in Gertrude's bedroom—pursuing their incestuous relationship—he kills Polonius instead.
In wanting to do the right thing, Hamlet proves he is a great man, though inexperienced in the ways of the world, especially life at court—he has been away at school. He is genuinely crushed by Ophelia's death, and saddened to have taken Laertes' father from him. Hamlet loves his mother but feels betrayed by her—however, he easily forgives her at the urging of his father's ghost.
His indecision (Hamlet's flaw) does seem to cost him his life: had he killed Claudius earlier, he probably would have survived. However, in all of this craziness, I feel badly for the young man who is called upon to sacrifice everything because his uncle is such a horrible man.
The post above identifies the primary aspect of this tragedy--that Hamlet is able, despite his many flaws, to avenge his father's death, though it costs him his life to do so. There are plenty of examples along the way, including all the opportunities Hamlet had to kill Claudius but did not. An ancillary tragedy is that Hamlet not only lost his own life but was also responsible, directly or indirectly, for the deaths of people he loves. That includes Polonious, Gertrude, Laertes, and Ophelia.
Possible thesis statements:
While Hamlet suffers a tragedy in death, he died as a hero, finally avenging his father's death.
Hamlet is a tragic hero because he dies while avenging his father's death.
Because Hamlet dies in the end, he is a tragic hero who dies while avenging his father's death.
Hamlet's death is truly tragic in that he dies while avenging his father's death.
Although Hamlet's life ends in tragedy, he dies as a hero while avenging his father's death.
You could get more specific and state what qualities of Hamlet make him a tragic hero and then your body paragraphs will find examples of those qualities and will examples how those examples prove he is a tragic hero. Your quotes need to come from your plot-line examples. Remember that tragic heroes are usually of noble class, have fatal weaknesses in their character, have strengths that become their weaknesses, create pity and fear in the audience, cause problems for others through their conflicts, etc. These are all things that you can explore in your essay.
I would analyze the essay making the Aristotelian definition of a tragic hero the touchstone.Ech aspect of the definition should be taken into account ,explained and elaborated with examples emphasizing his tragic flaw of lack of action and excessive contemplation and its tragic effect on the host of characters in the play including himself.