In Shakespeare's play, Hamlet, Hamlet certainly does meet tragedy. It begins before he even returns home for his father's funeral, when the tragic events of the story are set in motion by Hamlet's uncle, Claudius, who kills Old Hamlet and marries his widow.
From the instant Old Hamlet is murdered, Hamlet has no way to save himself. It could be argued by those who believe in fate (as Shakespeare seems to) that Hamlet's destiny was sealed at that moment. I believe that Hamlet really had little chance of taking on his uncle and surviving. Claudius is obviously a man with more worldly and political experience than Hamlet who has been off at school. Because Hamlet is surrounded by people who are loyal to the new King, Hamlet is isolated with his knowledge of his father's murder.
Hamlet cannot talk to his mother, Gertrude, who is married to Claudius: can she be trusted? Was she complicit in the murder? Polonius is a foolish old man who would do anything to ingratiate himself with Claudius. Rosencrantz and Guildenstern, Hamlet's "friends" from school, would sell their souls to earn the gratitude of the King. Laertes is away, and when he returns, the loss of his family members makes it impossible for Hamlet to trust him. Lastly, he wants to trust Ophelia, it would seem, but does not give her credit for being strong enough to remain faithful to him rather than father and King. She is ordered by her father and the King to report to them everything that Hamlet says, but had Hamlet explained that he felt endangered, with no mention of Old Hamlet's cause of death, Ophelia might have risen to the occasion to support him in his time of need.
With only Horatio at his side, Hamlet has little chance of being successful in bringing his uncle to justice without losing his life. By the end of the play, things are much worse: everyone but Horatio dies. Hamlet does, indeed, meet tragedy, killed by his uncle's treachery as Hamlet tries to avenge his father's murder at the hands of Claudius.