In Shakespeare's Hamlet, the character Hamlet is a tragic hero. He has a task to do, but a personality flaw gets in the way. Although he ultimately succeeds in avenging his father's death and cleansing Denmark of the evil, his waiting so long to do it causes a blood bath. Other people besides Claudius (the guilty party) die needlessly. This makes Hamlet, by definition, a tragic hero.
Your question, however, contains a number of layers. Hamlet is probably not an anti-hero in our modern sense, if that's what you mean by a "non hero." He isn't a good-hearted rogue, or an extremely flawed figure who just happens to do something heroic.
But is he a hero, in any sense other than as a tragic figure? He is brave and fearless at times, he is intelligent, he can be good hearted though he is merciless to those who betray him, he is deeply loyal to his father, and he is an excellent swordsman. He is good, if that's important to your definition of a hero.
In his environment and in his role, he is probably a great hero. He is royalty, and he avenges a king's murder. He is also, Claudius says, beloved of the Danish people.
I'll leave the conclusions to you.
Hamlet is not a hero, nor a tragic hero, nor a non-hero. He is a man. A man of intellect in a stupid world. A man of kind heart in a heartless world. A man of reason in a world without reason.
Hamlet is a sensitive renaissance intellectual forced to act in a medieval way. He is the ideal future man (from a 16th century POV) dragged mercilessly back into the violent past of his ancestors.
Hamlet as a hero is presented that he is loved by the people who rejoice his return home. Hamlet has been given the duty to avenge his father's death. He has been placed in a blood war that he must find a way to complete. Yet, he is a son who loves his mother but is confused by her actions at marrying his father's murder. (It is implied that the queen has no knowledge that this had occurred). His mother in praise to him accidentally drinks the glass of poison that had been meant for him.
Hamlet does draw back and forth as whether it is right or not to take the life of his step father, but in the end he does that which he believes he has been destined to do. He is a tragic hero but probably not one to Ophelia and her clan.
he is not a hero of actions ... he is only a man of words ... he is a hero in his ideas and his words ... he is a man with knowledge , a man with honor , a noble man , so if he acted like a hero in his actions and kill his uncle he wouldnt be the noble man that we all love ...
that is my answer
heyyy frizzy perm ur ssoo rite thats probably something i would put bout we can only say if he is a hero or non hero ssooo srryyy but thats a great answer :)))