After getting back from the unknown world, DMC will teach you a new move. I was never good at parrying anything so this guide will never ever use this skill. However if you're good at using it then feel free to do so.
After the short introduction to the new ability, start hacking away at the demons until you finish them all off. Remember to shift from one weapon to another and also aerial and ground combos to get a better mission rating.
Now head out through the only door in the area and Dante will look back and take a look at a photo on the floor. A short cut scene will play.
After the cut scene head to the left side of the door once you exit it and use the chandeliers to get to the other side.
Make your way throught the corridors and down the inclined one that leads down. You'll be sent back into the main hall area and you'll have to make your way across.
Jump and use your Angel lift to get to the other side. Once there use Demon pull to reveal another blue crystal that you can use Angel lift on.
Enter throught the door directly in front of where you used Demon pull and keep close to the left wall. The floor will start falling soon after that.
Make your way through the gaps and towards the light symbol on the floor to make it back to the real world.