What are key points to highlight in a short introduction to a review of the play Hamlet?
I'm a little unclear as to what you want. Do you want a short overview of the play? Or do you want a short introduction to your review of the play? Based on the wording of your question, I believe that you would like an introduction to your review.
Good introductions grab the reader in the first sentence. That is going to be important. You can do that by asking a question, using a quote, making a bold statement, giving a definition, or by telling another short story. I like to use the question or bold statement method because it gets me writing in my intended direction immediately. But the other methods are good too. Since you've said that your piece is a review, I'll assume that you are going to tell your reader why Hamlet is a good or bad play in your opinion.
You could mention that Hamlet is one of Shakespeare's all time greatest tragedies. It combines mystery, fantasy, action, and intrigue. You could also talk about how it allows audiences to witness Hamlet's deeply woven con to exact revenge against his step father.