Wuodan
Present Day. Present Time.
But DmC had to tweak bosses and in order to make them beatable with Vergil. That's why they made another Bloody Palace for Vergil instead.I thought that too when Vergil's Downfall came out. And look how it turned out: no Vergil in BP :/
In DMC4 though every boss and mob was already beatable with any of the characters and weren't specially designed for any.