As literaturenerd stated, describing one episode of Beowulf as more thrilling than another is based on one's personal opinion. In my opinion, the most thrilling episode of Beowulf is "Episode 11: Beowulf fights the dragon."
Beowulf fought the terrible Grendel and his mother when he was a young man, and many years have passed by this episode. Beowulf has become a great king, but he is old when the dragon arrives in his realm. Hero that he is, he leads his men out to fight the dragon anyway. His men are fearful, and only one--Wiglaf--is brave enough to accompany him into the dragon's lair. I find this thrilling, because I wonder: How can an old man like Beowulf fight a dragon, especially without the help of his army?
At first, it seems he might not prevail. His sword breaks when he strikes the dragon, and then the dragon injures him!
Then the terrible dragon
a third time rushed,
hot and battle-grim.
He bit Beowulf's neck
with sharp tusks--Beowulf
was wet with life's blood;
blood gushed in waves.
However, with Wiglaf's help, Beowulf recovers and strikes a death-blow on the dragon.
The enemy fell--strength
had driven out life;
the two kinsmen, together,
had cut down the enemy.
So should a warrior do.
Alas, Beowulf dies from his injuries, but he dies a noble death--a warrior's death. What episode could be more thrilling than this one?
I assume that by episode you are referring to the chapters of the text of Beowulf. Some versions of the epic text have been broken down into episodes by its translators. For example, one version of Beowulf possesses twelve episodes (as translated/adapted by David Breeden).
The naming of one episode being more thrilling than another is subjective (based upon one's personal opinion). For me, I believe that episode four is the most thrilling. In this episode, Grendel faces Beowulf. It is in this episode that Beowulf proves his intent to fight Grendel without weapons or armor (in order to maintain his aristeia (the hero's finest moment in battle) and arete (excellence)). Beowulf's battle boast to fight equally illustrates his true heroic nature. It is here where Beowulf's actions speak louder than his words.
This proves to be the most thrilling based upon the importance of one's faith. Not only does Beowulf state that he will destroy Grendel, he does so with the help of God and his God-given strength. Beowulf knows that he will only win if the victory is supported by God. Beowulf's actions, the shedding of weapons and armor, prove to be worthy of God's support.