Here's why:
* Polonius: While Hamlet does kill Polonius, it's not a premeditated murder. Hamlet mistakenly believes he is killing King Claudius hiding behind a curtain, and only realizes his mistake after the deed.
* Claudius: Hamlet does kill Claudius, but only after a lengthy scheme and elaborate trap. It's a revenge killing, and though Claudius' death is accidental in a sense, Hamlet still intends to kill him.
* Other characters: Hamlet kills no other characters in the play.
It's important to remember that Hamlet is a complex and deeply tragic figure. While he does take lives, his motivations are often driven by grief, madness, and a sense of justice. He is a character who grapples with morality and the consequences of his actions throughout the play.