You can control Vergil's Doppelganger when you're doing the Judgement Cut charging move. The Doppelganger is supposed to mimic everything that you do, so by having Vergil stuck in a charge move, you will "take control" of the Doppelganger instead. This requires a bit of cheating though, you have to confuse the game (by jumping a lot and alternating randomly between the different Doppelganger styles with the D-pad) so that the Doppelganger doesn't get stuck like you. However, you have to hold the attack button all the time, meaning you can't really attack with the Doppelganger. You can only use the circle/B and square/X button, but that's it. You can't jump either, otherwise Vergil will jump. Song is called The Barber Of Seville (Overture) by Gioachino Rossini.