Nero should be able to fight Dante, but should not be any match for him, as Nero is only human, and Dante is half-demon.

So Nero, after being defeated, is banished by the Order of the Sword, sets out to find Dante, and get back his title in the Order, by killing him.

Eventually, Nero meets Vergil, recently freed from Mundus' seal by Dante. Vergil, looking to avenge his defeat by Dante from Devil May Cry 3, joins up with Nero.  Eventually, the 2 of them confront Dante.

They fight him, and have the upper hand, until Dante goes into his Desperate Devil Trigger, and defeats both of them. Then Dante notices that Nero is being possessed by Mundus, and tells Nero to fight it.

Nero fails, and Mundus takes over. Mundus proceeds to defeat Dante, kill Vergil, and slaughter the Order of the Sword, including Katie, Nero's wife/ girlfriend, and she dies believing Nero to be a traitor.

Dante manages to reach the Order's HQ, and revives Sparda, to save the world.

But instead of appearing in person, Dante recieves Sparda's full power, and uses it to finally kill Mundus for good.

Nero dies in Dante's arms, and Dante is greatly saddened by the promising young demon slayer's death.

He hardly ever speaks after that.