Act 3 Scene 4 Hamlet firmly addresses his mother in her room, and at one point, she is afraid he will attack her. Polonius calls for help from behind the curtain and Hamlet stabs him. Hamlet forces Gertrude to see how bad her relationship with Claudius is compared to Hamlet makes her promise to not sleep with Claudius anymore and leaves with Polonius' body.
Act 3 Scene 2 Hamlet torments and humiliates Ophelia in front of others with vulgar jokes to keep up his image of being "mad". During the play, Claudius is so ridden with guilt he cannot even remain in the room. This moves Hamlet to believe Claudius guilty of murder, and so he later concludes that he has to shake his mother back to her senses.
Act 3 Scene 1 Claudius wants to send Hamlet to England. Polonius plans to hide behind a curtain in Gertrude's room to overhear their conversation. Claudius kneels as if to pray and acknowledges his wrongs but ultimately decides not to repent; Hamlet decides not to kill Claudius otherwise he'd send him to heaven and Hamlet to hell.