In my own conceit, Hamlet is a tragic hero and the reasons are as follows.
Hamlet, as the highborn prince of Denmark, is well-educated and respected. He has good views on humanity: “What piece of work is a man, how noble in reason, how infinite in faculties, in form and moving how express and admirable, in action how like an angel, in apprehension how like a god: the beauty of the world, the paragon of animal”.  While Hamlet himself, according to Ophelia’s words, is “The courtier’s, soldier’s, scholar’s, eye, tongue, sword, th’ expectancy and rose of the fair state, the glass of fashion and the mould of form”. Undoubtedly, Hamlet is an ideal man and the embodiment of virtues.
However, the world is “An unweeded garden that grows to seed; things rank and gross in nature possess it merely”, and “A goodly one, in which there are many confines, wards, and dungeons, Denmark being one o’ th’ worst”. The reality soon revealed the dark side of human nature to Hamlet: in the royal power struggle, Hamlet’s beloved father is assassinated by his uncle, Claudius. For Hamlet, the love is not faithful: two months after King Hamlet’s death, the Queen remarried with the evil King, as she “post with such dexterity to incestuous sheets”; while the friendship is also not reliable: his two good friends become the spies to detect his behaviours. As how Hamlet would describe: “The time of out of joint”!  Meanwhile, Hamlet is given two important tasks: one is to revenge for his father, the other one is to “set it right”. For Hamlet, these two tasks may be too heavy.
Besides, Hamlet’s own weakness also caused his tragedy. Hamlet is a great thinker but a bad doer, while he often miss the chance while he determined to act. King Claudius praying after watching “ the Mouse Trap” Play should be a great chance to assassinate Claudius. Nevertheless, Hamlet is thinking: “And am I revenged, to take him in the purging of his soul, when he is fit and seasoned for his passage?” Such useless consideration made Hamlet miss the best opportunity to kill the King. Eventually, his hesitation caused his death.
To sum up the above arguments, Hamlet is a tragic hero.