How did Beowulf's desire for glory cause him to act in heroic ways?
Although Christian themes exist alongside pagan themes in Beowulf, a warrior might hope to obtain immortality by performing brave deeds and thus, live on in stories and human memory. Living on in history and human stories, not necessarily heaven, was the glory of immortality.
And while Beowulf performed heroic deeds for glory, he also did so out of a sense of duty. On one hand, this was out of a sense of duty to Hrothgar. On the other hand, one could argue that Beowulf performed heroic deeds as if it were his fate (wyrd) or a spiritual calling.
That being said, in the context of the Beowulf manuscript, being a good king meant being kind to his people and being a good warrior meant loyalty to his lord. So, Beowulf was a brave warrior because he did want to be remembered as a courageous warrior and later, a generous king. But he also acted out of a sense of duty, loyalty, and purpose (this could be a moral code, a spiritual inkling, or a personal drive).