<em>"Trapped under the blanket"</em> is an adjective phrase.
An adjective phrase is a group of words which describes a noun/pronoun. It can be placed before or after the noun/pronoun it modifies. The adjective phrase, in this sentence, provides more information about the noun 'bug.' It tells us in which situation the bug found itself - it is trapped. It also tells us its location - under the blanket.
Beowulf's deeds require tremendous courage. Beowulf's deeds require courage, because Beowulf was courageous enough to death with Grendel's mother. And almost of the deeds Beowulf's require courage.
