This is a good question. It is probably a good starting point to list the three battles. First, Beowulf fights Grendel. Second, Beowulf fights a more powerful foe, Grendel's mother, who is filled with rage over the death of her son. Finally, Beowulf fights his most formidable foe, the dragon.
In each of these battles, Beowulf shows his courage and martial prowess. He does not back down and he accepts the challenges. From this perspective, the story develops his character as a veritable warrior. What makes all of these episode even more powerful is that he battle these foes alone or he is not afraid to fight them alone. So, he distinguishes himself from others, who might be afraid. Finally, he dies in the last battle, which shows that he even dies as a warrior with honor.