Beowulf and fame

I think that Beowulf is a little selfish in his quest for fame. Even before Beowulf defeats Grendel, Grendel's mother and all the underwater beast, he is already famous. When he fights Grendel, he knows he can show off his strenght by triumphing him with no weapons. He boasts about his power and brutality by saying " They have seen my strength fo themselves, have watched me rise from the darkness of war, dripping with my enemies' blood.... Now Grendel and I have come together, and I've come." (lines 418-426). Beowulf is already famous, but he continues in his hunt to impress the people even further. As he continues to fight, his popularity grows and so does his ego.