I would argue that there is no hero as such in Paradise Lost. Satan undoubtedly shares some heroic characteristics in his defiance of what he sees as God's tyranny and his unjust treatment at the hands of the Almighty. But in general, Satan is very far from being a hero in any meaningful sense of the word. For one thing, the speech he gives to his acolytes in Book II is full of vainglorious delusions, a desperately self-serving attempt to mitigate his humiliation at being cast down:
Farewell happy fields
Where joy for ever dwells: hail horrors, hail
Infernal world, and thou profoundest hell
Receive thy new possessor: one who brings
A mind not to be changed by place or time.
The mind is its own place, and in itself
Can make a heaven of hell, a hell of heaven.
What matter where, if I be still the same,
And what I should be, all but less than he
Whom thunder bath made greater?
Satan's putting a brave face on it, but we're not really convinced. He gives the game away by referring to the "happy fields" and "joy" of Heaven. Metaphorically, he's reduced to an impotent shaking of the fist at the sky.
In response to those such as Shelley or William Blake, who regarded Satan as the hero of Paradise Lost, we should bear in mind the moral degeneration that he experiences as the story unfolds. As C.S. Lewis once said, Satan goes from hero to general, from general to politician, from politician to secret service agent, from a secret service agent to a thing that peers through people's windows before becoming a snake and then a toad. Hardly heroic, one might think. Traditionally, a hero in Greek mythology was a character who took everything the gods had to throw at him before emerging triumphant, noble, and strong. Satan doesn't come anywhere near this standard of heroism, falling further and further away from God as he descends deeper into darkness.
This issue has been debated for several centuries among literary critics. In one sense, one could argue that Paradise Lost is not written in the form of either a tragedy or an heroic epic, and thus that there really are no "heroes" in the traditional sense in the work.
The protagonist of the poem is Lucifer, the brightest of all God's angels, who due to his disobedience to God was cast out of Heaven into Hell. Many critics consider Satan the hero of the poem, as the main theme of the poem is Satan's fall.
Although Jesus only play a minor role in the narrative, perhaps the most heroic act of the story is the decision of Jesus to sacrifice himself for humanity, but this only occupies a small part of the narration at the end of the book.
Although God is obviously the greatest and most perfect character in the story, because of what theologians term his impassibility (inability to suffer), God, being purely divine and not needing to struggle against human limitations, cannot really be considered a hero.