Another method of attacking this prompt might be to analyze the cost of revenge on the avenger. You might discuss the sacrifices that Hamlet must make in order to gain revenge on Claudius: his relationships with others, his mental well-being, and ultimately his life. You might conclude by evaluating if the revenge warranted the price that Hamlet paid.
Another way of looking at this prompt is to look at the several commands that the ghost gives Hamlet in seeking revenge. He tells Hamlet to avenge his "most foul and unnatural murder," but in so doing, Hamlet is not to "let his soul contrive / Against thy mother," he is not to let the "royal bed of Denmark be / a couch for luxury and damned incest," and he is not to "taint his mind." How well does Hamlet carry out these commands? Is Hamlet a dutiful son? Does the ghost expect too much?
You could compare and contrast Hamlet’s comments about revenge to Laretes’s comments about revenge. Both have the same objective. They both want revenge for their father’s murder. From the beginning of the play Prince Hamlet wants to get revenge on Claudius for killing his father. Laertes returns from France to get revenge for the murder of his father, Polonius. You should look at Hamlet’s comments when he speaks to the ghost and his soliloquies in acts I-IV and the comments Laertes makes in act IV, scenes v and vii. You can focus each paragraph on the following: revenge, self and personal commitment.