In Hamlet, Laertes' objective is to kill Hamlet. Hamlet has destroyed Laertes' loved ones. Hamlet kills Laertes' father, Polonius. This in turn destroys Laertes' sister Ophelia. Ophelia takes her own life due to anguish over losing her father by a man she loves.
No doubt, Laertes has a goal and strong purpose for killing Hamlet. One man has brought about his destruction. Now, to kill Hamlet will avenge Laertes' father's death. To kill Hamlet will restore Laertes' troubled heart because of the death of his father and sister.
What could be more important than to kill the one man responsible for destroying one's family? Laertes has a clear vision. He desires to kill Hamlet for making his life miserable through the loss of his family members:
Ophelia has gone insane after Hamlet’s departure and her father’s death. Laertes returns and vows to avenge Polonius’s death. Claudius contrives a fencing match between Hamlet and Laertes, during which Hamlet is to be injured with a poisoned sword tip and poisoned with a drink, thus assuring his death. When news arrives that Ophelia has drowned herself, Laertes is grief stricken.
To find relief for his troubled heart, Laertes agrees to fight his enemy Hamlet:
Hamlet’s confusing and truncated relationship with Ophelia and his inadvertent murder of Polonius have made the two young men virtual enemies.
In the end, Laertes accomplishes his main objective--he kills his enemy Hamlet.