There are literally dozens of topics about which you can build an essay pertaining to Hamlet. Below are some suggestions. Feel free to ask me about a topic not included in it.
While Hamlet often suppresses his passion for reason, ultimately it is his passion that leads to the deaths of the other characters. Explain.

Hamlet, Laertes, and Fortinbras each pursue vengeance in similar circumstances (dead father, tainted family honor), although the methods each chooses and its ultimate result is different from the others’. Compare the approaches used by each character, evaluating the strengths and weaknesses. To you, which was better? Why?
All tragic heroes in Shakespearean drama possess a hamartia (fatal flaw). This character trait is both that character’s greatest strength yet also results in his/her downfall. Define what you believe to be Hamlet’s hamartia (he recognizes at IV.iv.38-45) and show how he does not procrastinate because of this flaw.

Examine the roles of Gertrude and Ophelia. Are they merely secondary consideration which the play could do without OR do they clearly move the plot forward and make the play more interesting. Be specific in exploring key scenes in which they are involved.