What does the speaker mean when he states that Beowulf's men are "trying to open / A path for his evil soul”?

it means they are letting in evil

This would now be an adverb because it’s explaining the action verb. If you were to say “she has taken exercising to a new extremity,” the extremity is explaining the manner the action verb is in, making the most sense. The noun is “she,” the verb is “exercising” so the only option left really is for it to be an adverb.