Anne demonstrates one of human beings' greatest frailities - vanity. She is perfectly aware of Richard's evil and murderous nature, but Richard is cunning. He approaches her with calm sincerity, not attempting to deny her accusations, knowing that anyone who is denied (put on defense) only becomes more angry.
Richard then is the sweet-talker, first flattering her dead husband, whom she obviously loved. Richard states he was "fitter for [heaven] than earth.]" He then moves on to Anne herself, insisting to Anne that she is the one at fault. Her beauty drove him to it. Who could resist such attention? Anne is resistant, even horrified at first, but the sincerity in Richard's speech i stoo much to overcome. He does not over-exaggerate, nor is he off-handed in his remarks.
Finally, when her defenses become lowered, Richard abandons flattery for another human weakness - compassion, and sympathy. He prostrates himself before her, telling her to kill him if she will. Seeing another human being subjugate himself, seeing another human in pain, would only fail to effect the most cold-hearted amongst us. Anne is easily won over.