As seen in Beowulf, what internal conflict does the epic hero face?
While not obvious, the internal conflict of the epic hero in Beowulf lies in the fact that Beowulf must defeat Grendel. Beowulf has traversed the seas to come to the Danelands in order to support his renown of being a great hero. That said, Beowulf does state that only God will determine who exits from the battle as victorious.
Even though Beowulf gives the power of the battle over to God, it cannot go without saying that he does has something to prove. In fact, his greatest internal conflict may lay with Unferth's antagonizing of the hero.
After Beowulf introduces himself to Hrothgar, Unferth "calls Beowulf out." Unferth states that he heard that Brecca won the race, not Beowulf. Beowulf then goes on to explain the actual outcome of the race. He (Beowulf) also recognizes the fact that Unferth is drunk and cannot be held completely accountable for his words.
Therefore, while Beowulf knows that he is capable of beating Grendel, one could support the fact that he does possess some internal conflict regarding Unferth's accusations. If he fails to beat Grendel, Unferth could be proven correct (saying that Beowulf is not a true hero). In this sense, it could be at the back of Beowulf's mind (although never technically brought up in the text itself). In the end, if Beowulf fails to defeat Grendel, his acknowledgement as a hero would be in jeopardy.