1. Mourn his father properly: Hamlet believes Gertrude's hasty marriage to Claudius is a betrayal of his father's memory and a sign of shallow grief. He wants her to acknowledge the depth of her loss and show genuine mourning.
2. Repent her actions: Hamlet sees Gertrude's marriage to Claudius as incestuous and morally wrong. He wants her to repent for her actions and recognize the sin she has committed.
3. Distance herself from Claudius: Hamlet sees Claudius as a villain and wants his mother to cut ties with him. He believes she is being manipulated and controlled by Claudius and wants her to see through his facade.
4. Understand his pain: Hamlet is deeply hurt by his mother's actions. He wants her to understand his pain and the emotional turmoil he is experiencing.
However, Hamlet's approach is often harsh and accusatory. He verbally attacks her, calls her names, and threatens her. This makes it difficult for Gertrude to fully understand his desires and respond in a way that satisfies him.
Ultimately, Hamlet wants his mother to recognize the gravity of the situation, to take responsibility for her actions, and to choose a path that aligns with her conscience and true feelings. He wants her to stand by him and help him expose Claudius's crimes.
It's important to note that Hamlet's perspective is deeply affected by grief, anger, and a sense of betrayal. His actions and words are driven by these emotions, making his desires complex and sometimes contradictory.