The fact that Beowulf is killed shows that he is an imperfect hero not an infallible one. He is described as someone greater than al other men. Beowulf is honorable because he is courageous and a fighter. When Beowulf realizes that the battle with the fire dragon will go against him he continues to fight. That's why he is a hero on a quest.
I have this for my English class and i did the quizzes and my Topic test for Beowulf and i got 80% which is a good grade. I hope this will help you :)