As seen in chapter six of Beowulf, Beowulf declares his exploits as part of his introduction to Hrothgar. What do his exploits suggest about his character?
Chapter six of Beowulf provides Beowulf's introduction of himself to Hrothgar (king of the Danes). During this introduction, Beowulf tells Hrothgar about all of the challenges and victories he has has in order to support his renown. Beowulf tells Hrothgar about bloody battles with men, giants and beasts. In every battle, Beowulf emerged victorious. While some may interpret this laundry list of victories as Beowulf's lack of humility, another interpretation can be proven.
Beowulf is in the Danelands to help Hrothgar rid his country of evil (specifically, Grendel). In order to prove his ability, Beowulf tells Hrothgar about all of the trials and challenges he has faced. With each of these challenges, Beowulf's foes found themselves "witnesses" of their own demise as they saw Beowulf "flecked" with their blood.
Therefore, although some would say that this introduction proved Beowulf's character to lack humility and humbleness, it actually proves his confidence and ability.