By the end of Act III, Hamlet has a renewed resolve to slaughter his uncle as revenge for murdering his father. Although he hesitates when he sees Claudius praying—as he does not want to send Claudius to heaven when his own father was sent to Purgatory with all his sins unabsolved—he acts quickly when he believes Claudius is eavesdropping on his conversation with Gertrude, his mother. Polonius, Claudius's adviser, is hiding in Gertrude's room, and when Gertrude gives voice to her fear of Hamlet, Polonius cries out. Hearing this, Hamlet asks,
How now, a rat? Dead for a ducat, dead! (3.4.24)
Hamlet stabs the hidden Polonius, believing it to be his uncle, Claudius, and then he shows absolutely no remorse for the action once he discovers his mistake. Hamlet, at this point, seems quite willing to get his hands dirty and to take more decisive action against his uncle than he has previously. When his mother points out what a rash and terrible thing he's done, he asks her,
A bloody deed? Almost as bad, good mother,
As kill a king and marry with his brother. (3.4.29-30)
He is disgusted with her. He accuses her of lacking modesty and innocence and loyalty because she married her husband's brother so soon after her husband's death. As a result, Hamlet asks her,
O shame, where is thy blush? (3.4.82)
He cannot believe that she doesn't feel ashamed of herself and her behavior. Hamlet seems most disgusted by the fact that Gertrude sleeps with Claudius, and he advises her to no longer allow him into her bed.