In Paradise Lost by Milton, what characteristics does Satan have that make him a hero? How does Milton's Satan compare to Beowulf as a hero?
First, we should distinguish between two terms, "hero" and "protagonist." A protagonist is the most important character in a story but can be admirable or despicable or sympathetic or abhorrent. A hero is a protagonist with some type of greatness beyond that of the ordinary mortal, with whom we generally sympathize. Satan's role in Paradise Lost is complicated, not precisely that of a hero, although sharing some characteristics of certain heroic types. Blake and Shelley, who themselves were strongly anti-Christian, interpreted Satan as the hero of the poem, but most critics see their readings as based more in their own ideological concerns than justified by the text. Scholars have debated the question of who counts as a hero in Paradise Lost and the general consensus is that there is no classical heroic figure, but that certain heroic elements can be found in the Son of God, Adam, and Satan.
Milton was a Puritan, a devout Christian espousing a strongly Calvinist form of Protestantism. There is no evidence that Milton himself admired Satan or himself rebelled against God (his other writings suggest deep and sincere piety). There is, however, a literary problem with making God a hero. What makes a narrative interesting is a plot structure in which there is a genuine conflict and normally some sort of obstacle for the protagonist to overcome. Since God is omnipotent, omniscient, and incapable of suffering, God's very perfection as a deity makes him a very dull protagonist indeed; while the Son can be a hero because he will eventually struggle and suffer, and Adam is a mortal who suffers, God the Father cannot be a hero.
Satan as a protagonist captures the imagination in the same way as some of the evil tragic heroes such as Clytemnestra and Medea or Shakespeare's Macbeth. He does not resemble an epic hero such as Beowulf at all, because he is not a force for good or supporter of legitimate authority. While he shares the heroic characteristics of power and strength of body, will, and intellect, he is, within the worldview of the poem, completely and irredeemably fallen. Like many villains, he does tend to get the best lines of the poem and is a character most readers find appealing, but more in the style of a seductive villain than a hero.