What are some examples of Beowulf being fearless during his battle with Grendel, Grendel's mother, and the dragon?

The fact that Beowulf is fighting any of these foes is a
testament to his fearlessness.  He chose to go defend Hrothgar against Grendel; because
of that, he had to fight Grendel's mother; because of that, undoubtedly, he was named
successor to King Hygelac and fought the battle against the dragon to protect his
people.  That being said, there are some specific examples of fearlessness in
Beowulf.

First, he chose to fight
Grendel without weapons.  He made that choice because that's how Grendel fights;
however, he was under no obligation to treat this enemy with honor, since Grendel was a
marauder who had no intention of ever "fighting
fair."

Second, he actually followed Grendel's mother to the
bottom of the ocean to her lair.  She wasn't chasing him, nor was he in any danger from
her.  Instead, Beowulf recognized the potential of another monster attacking Hrothgar's
people and decided to preempt her attacks by killing her before she
started.

Finally, Beowulf attacked the dragon in a
single-handed combat.  This is an imposing fifty-foot-long, fire-breathing dragon who
has been roused to anger.  Beowulf says,

readability="11">

...when he comes to
me

I mean to stand, not run from his
shooting

Flames, stand still till fate
decides

Which of us wins.... (line
2525-2528)

That's what he
says before the battle, and that's what he does.  He never backs away, even though his
death is imminent.

These are three of Beowulf's biggest
battles, and he fights each of his foes fearlessly.