One aspect of Beowulf that has always intrigued me and that you might want to explore is the Christianization of a Viking saga. Is Beowulf a great hero because of his strength and courage or because God has given them to him? With the Christian elements added, is Beowulf truly a traditional epic hero?
Consider as well, instead of identifying the details of an epic hero, identifying the details of an epic and developing an essay in which you explain how Beowulf fits the definition of an epic.
The definition of an epic can be found here:
You could make a critical essay in which you explain why Beowulf is a good epic hero or why he is an unsuccessful hero.
I am not sure I understand your question exactly but you could write an essay on how Bewulf fits the tradition of an epic hero. A description of the general characteristics of an Epic hero can be found at http://www.victorianweb.org/genre/epic2.html.
You could also look at the essay questions in the Sample Essay Outlines in the Beowulf enotes. http://www.enotes.com/beowulf/sample-essay-outlines
Another suggestion is that you could trace one of the themes of the work as discussed in the section on themes in the Beowulf Enotes: http://www.enotes.com/beowulf/themes
Let me know if I can be of any further help.