the theme of life/death
This is not really a theme... I mean, it is, but when I think of a theme for an essay I think of a unique observation. Think of it this way... those links above will take you to discussions given by some people who know Shakespeare's work very well. Other people who know it well will have different opinions. If you know it well, you will have your own unique opinion. Your opinion will be unique because it is like this:
Shakespeare's writing X Your personality = a unique insight.
Express that unique observation at the end of the first paragraph.
You might need to read several analyses. In addition to the links provided by Nata, Google this:
Hamlet character analysis