"Beowulf demonstrates how a hero can achieve a sort of immortality even if he is doomed by fate to die in battle."I have to write an essay, but I have no idea how to begin this!
You might want to respond to this question by refering to the heroic code that is developed and explored in this epic text. Every position in this world has characteristics that emerge from this code and serve as pointers towards whether actions support or break this heroic code. For example, warriors are expected to be strong, courageous and loyal, and kings are to be generous, politically astute and hospitable. Of course, this actually presents us with many ambiguous situations in the text where the limits of this heroic code are presented and questioned. Key to this issue is the choice of Beowulf to go and fight the dragon, even though he knows that this will result in his death, leaving his people defenceless and without leadership at a critical juncture for his nation. Does Beowulf do the right thing? Every reader will have a different response.
Clearly, you could argue that the statement can easily be supported by the way that the legend of Beowulf is still being studied and read today. In spite of his death, decreed by fate, he has, nonetheless acheived a measure of immortality through his bravery. However, as my points above suggest, whether Beowulf was truly heroic in going to meet his doom is another matter.