Answer:
Hamlet´s main goal is avenging his father’s being killed. There are no hints that imply him angry about not being king following his father’s dying. What he wants is to make sure that Claudius is guilty and kill him as retaliation to send him to hell.
Step-by-step explanation:
In act 3, Hamlet has an opportunity to kill him, but since Claudius was praying at the time, Hamlet feared that killing him would send him to heaven, so he didn´t. That implies that the ultimate revenge for him is sending Claudius to hell. Ophelia and her romantic relationship with Hamlet play an important part in the plot of revenge. In the end, is the fear of others to Ophelia being with Hamlet, as well as Hamlet´s erratic behavior around her, that drives Ophelia mad into killing herself.
Hamlet seems to have clear goals but finds he´s unable to accomplish them because of doubt and erratic behavior while trying to discover the truth about his father. While he goes through a justified and not greedy attempt to seek revenge and seems to be in love with Ophelia, his actions don´t allow him to accomplish his goals.