beowulf says that he has come to kill Grendal. What proof does he offer that he is up to the task ?

Beowulf is the typical Anglo-Saxon hero who can recount all of his prior adventures. He has fought for his people in the past - he has come again to help those in need. He comes to rescue Hrothgar from the "monster" - his strength is unequaled and he believes in himself. This is his proof. He has won contests in the past (swimming), and like Anglo-Saxon heroes he believes in his ability to kill Grendel.

Beowulf is a young Geatish warrior that is famous for his war-like escapades. Beowulf is like this super alpha-viking that volunteers to come and fight the monster.