Beowulf is an Anglo-Saxon poem in which the epic hero Beowulf saves Hrothgar and his people from the tribulations which had beset them. Beowulf is a conquering hero, and he embodies, as your question states, many of the ideals reflected in his culture. He is selfless, proud, brave, and loyal.
Beowulf is selfless, and he demonstrates that quality when he hears about Hrothgar--in a country across the dangerous sea--and decides to help him simply because he knows he can. Beowulf understands he may not return from this fight that is not really his; yet he selects a few soldiers, equips himself and his men, and he makes the perilous crossing without any expectations from the people at the other end of his journey.
Beowulf is proud, and he demonstrates that quality when he meets Hrothgar and offers himself as a protector and defender of this king and his people. He is neither fawning nor boastful (though Unferth would probably disagree). He states his credentials and offers his services. Later, when Hrothgar rewards him for his actions, Beowulf is suitably gracious and humble, proud to have been the one to rid them of this terror. When he returns home, he tells his story without embellishment (well, perhaps just a little) and demonstrates his pride by honoring his own king.
Beowulf is brave. A marauding monster, Grendel, must be killed, and Beowulf chooses to engage in battle without any weapons, just as Grendel fights. Their literal hand-to-hand combat is epic, and Beowulf wins by tearing Grendel's arm out of his socket. When Grendel's mother seeks to avenge her son's death, Beowulf follows her to the bottom of the ocean to fight another epic battle. More than fifty years later, King Beowulf fights a huge dragon virtually alone and virtually empty-handed.
Beowulf is loyal. Before he leaves to kill Grendel, Beowulf asks permission of his king--to whom he owes his allegiance. When he returns, laden with gifts which were bestowed upon him by a grateful Hrothgar, Beowulf gives a portion to his king, as was his due.
Beowulf has other virtues, of course, and he embodies the best of Anglo-Saxon ideals.