Beowulf offers several proofs that he is up to the challenge of killing Grendel:

• He insists on fighting Grendel without weapons, believing it honorable to match the monster's unarmed nature, which shows his confidence in his own strength and skill

• Beowulf demonstrates extraordinary physical power by wrestling Grendel and ultimately tearing off the monster's arm with his bare hands, a feat no other man has accomplished

• He has a reputation supported by stories of his previous battles with men and monsters, which he recounts to assert his capability and readiness for this challenge

• After the fight, Beowulf displays Grendel's severed arm publicly in Heorot as tangible proof of his victory and to assure the Danes that the threat is ended

These actions collectively prove Beowulf's courage, strength, and honor, establishing him as capable of defeating Grendel.