What are some good ideas for an argumentative essay on Hamlet?

For any argumentative essay, you need a thesis statement (topic). In the first paragraph, you want to start with a general introduction of a few sentences about your topic. Then, state your thesis. Then, explain why the thesis is significant, interesting, relevant to the play, or relevant to a particular interpretation of the play. 

Hamlet's "delay" is a popular topic and many essays and articles have been written about it. A first paragraph on this...

For any argumentative essay, you need a thesis statement (topic). In the first paragraph, you want to start with a general introduction of a few sentences about your topic. Then, state your thesis. Then, explain why the thesis is significant, interesting, relevant to the play, or relevant to a particular interpretation of the play. 

Hamlet's "delay" is a popular topic and many essays and articles have been written about it. A first paragraph on this topic needs to start with the general introduction, followed by the thesis statement, and then the significance of that thesis statement. I will use a logical introduction with a ridiculous thesis (in bold) statement just to show the structure of this opening paragraph: 

Hamlet must kill Claudius to avenge his father. He delays this vengeance repeatedly and this procrastination has been the subject of debate for centuries. Why does he keep putting it off? I would argue that whenever Hamlet sees Claudius in person, something triggers in his mind and he sees Claudius as a cute and fuzzy bunny. Hamlet has been hypnotized to see this hallucination by Polonius. Seeing the bunny (Claudius), Hamlet is simply unable to murder it (him). This, of course, drastically reinterprets the play and totally changes the traditional perception of Polonius's role in the play. 

In subsequent paragraphs, you want to find evidence from the play to support this thesis. It would also help to use secondary sources (articles) that argue in favor of your thesis. Quote these articles if necessary in the proper paragraphs. After that, provide one or more paragraphs of arguments that disagree with your thesis. Show how these arguments are false.

Use a final paragraph to state your conclusion. Note: do not just restate your thesis at the end, word for word. Restate your thesis by briefly explaining how your evidence supports it. State something like, "It is plausible if not certain that Polonius hypnotized Hamlet to view Claudius as a cute, fuzzy bunny in Act II. As an ally of Claudius, this was Polonius's way of protecting the king and making a fool of Hamlet in the process. The evidence I've provided lends more credence to the so called "Bunny Theory."