How is Beowulf an epic?
The best way to answer this question is by looking at other epics, such as the Iliad and the Odyssey. If we do this, there are several features that make Beowulf an epic.
First, Beowulf, like the Greek epics, deals with a hero and a voyage. Like Achilles and Odysseus, Beowulf is on a journey. Beowulf goes to the land of Danes to fight the monster, Grendel, and later he fights the dragon.
Second, this might sound odd, but many epics start off as oral poems. Beowulf shares this in common with the Iliad and Odyssey, which come from oral tradition as canonized by Homer. Related to this point, Beowulf, like the other epics, is written in poetry. Homer's words are written in dactylic hexameter and Beowulf in alliterative verse or alliterative poetry.
Third, there is a major contest in view, which is usually for glory. Beowulf fights two foes - Grendel and the dragon. Achilles fights Hector, and Odysseus fights the suitors.
In light of these point, Beowulf certainly qualifies as an epic.