Beowulf shows himself to be a brave young man desperate to prove himself as a warrior. Despite his relative youth, he knows that he is different from other men, and that if anyone can defeat the blood-thirsty monster Grendel, it's him. Beowulf is also possessed with excess pride. Ultimately it will prove his undoing when, as king of Geatland, he will engage in one fight too many. But for now, Beowulf's hubris enables him to perform truly epic feats of daring, like swimming for five days and nights in icy seas while carrying a sword, and battling deadly sea monsters.
As well as arrogance and boastfulness—witness his outrageous disrespect of Unferth—Beowulf's excessive pride leads him to answer Hrothgar's SOS call without a moment's hesitation and head on over to Denmark to slay Grendel. Beowulf may be boastful and positively bursting at he seams with pride, but he's not like Achilles; he does have a wider sense of responsibility to others.