Even in death, he would believe it to be a fitting death for a soldier because he would be remembered for ages to come anyways.
This idea of the outcome possibly being grim for Beowulf during battle has been shown throughout all his moments prior to when he fights. Beowulf emphasizes that his life would be endangered again, when he is at the feast and says that his “purpose was to win the goodwill of Hrothgar’s people or die in battle, pressed in Grendel’s fierce grip.” Again, he knows that he is only mortal, regardless of his immense strength and his past battles, in which he has slain sea monsters after sea monsters, there is always a chance that he may die. It would not be because he was weak, but simply because his time has come, as a mortal, in the eyes of God and fate.