Ninja Theory has detailed Vergil's Bloody Palace for DmC: Definitive Edition in a new video which you can see above.
The Bloody Palace battle arena covers 60 floors and works through the game's five main difficulty levels. Beginning at Nephilim difficulty for the first 20 levels, the mode then moves to Son of Sparda, and the final 20 levels are on Vergil Must Die difficulty.
Ninja Theory's Dominic Matthews told the PlayStation Blog:
"The best way to play Vergil is to stack up as many kinds of damage as possible. He has lots of attacks which skilled players can layer with his melee moves. For example, Summoned Swords can be fired, and can pull enemies or lift to enemies, without interrupting melee attacks. Spiral Swords passively damages enemies once activated, until it wears off. Doppelganger Vergil can be used to attack at the same time as you, or with a delay."
When everything is powered-up, Vergil can use multiple attacks at once and this is unsurprsingly when he causes the most damage. As ever with DmC, style will play a roll in how you're scored.