As soon as the level starts make your way to the next platform. The floor will start falling so you need to be quick about this. If you're too slow then you can potentially fall and repeat the whole thing again.
Use Angel lift then activate the boost rings to get to the further end of the area.
When the floor starts falling faster than you can make it to the other one, use double jump and Angel boost to propel yourself to the next platform.
Don't stop running until you reach the Angel lift marks that lead to the building entrance.
Once you get to the entrance you'll be required to kill some demons while Vergil makes his way through the security system.
You'll be put up against a stronger version of the Stygians, the Elite Stygians. Which is basically like a Stygian but with a longer blade and a stronger attack. Other than that they're like Stygians.
Finish them off quickly and a Witch will appear. Throw your Aquila at the with to break her shield, then pull her in closer to finish her off. Once the Witch is dead take care of the remaining Elite Stygians.
After killing off the last wave of demons the entrance will open and you'll be given 30 seconds to get your ass in there. You don't have to kill the demons that will spawn and attempt to distract you. Just run towards the entrance of the building.
Inside you'll be attacked by one of the masked swordsmen that always seems to run whenever you hit them enough. Dreamrunner, is basically the same as the previous one except he will deflect your blow if you fail to hit him three times. Meaning you can't afford to just blindly attack him.
There's only 2 ways you can ever land a hit on this guy. First is to dodge his attack and get behind him, you'll have to be quick about this meaning when you dodge it has to be precise and you aren't too far. If you land a blow at his back or his side it will damage him.
Second if you're good at timing and parrying, you can parry his attack when he disappears into the portal. Face the new portal and attack him with Rebellion at just the right time to stun him.
Either ways whichever method you use start attacking him with Rebellion once his defence is down. Keep on repeating it until he's dead.
Head inside the only open door and get into the elevator. It will automatically take you up into the 87th floor where you'll reunite with Vergil for a short time.
After the cut scene head into the east wing as KAt instructed and you'll be attacked by a Ravager and 2 Elite Stygians near the end of it. My favorite way to take care of these guys is to use a fully charged Aquila and once they're caught in it I use Rebellion's Drive ability to kill them quickly.
Once you get inside you'll notice that the path has a laser system. Vergil will knock them out for you and you'll be able to make your way to the next building.
Inside the finance wing you'll be attacked by a Dreamrunner and a pair of Bathos. Take care of the Bathos first or this can get ugly. Pull on their shield with Demon pull and finish them off with an attack from Eryx or Arbiter.
Once the Bathos are gone focus on Dreamrunner. The same tactic will work on him and you're also given an alternate way to attack him. Ping Pong is a useful skill if you have Arbiter's axe throw skill.
Use Angel lift on the section of the wall to get to the 88th floor. Head to the right once you get there.
You'll be attacked by 2 Rages and throw a couple of Aquila bindings at them then charge the Aquila and throw it at the Rages. That should keep them at bay for a while. You can start hacking at them now until they're dead.
Now enter the elevator on the right side, don't try to get inside the one with white light it will damage you. Once you're inside the elevator it will automatically move on to floor 105.
Once you're at floor 105 we find out that Dante is an idiot. Anyways turn to the left side and you'll be attacked by a couple of Stygians.
A good way to kill them off quickly is by using Aquila's buy in skill (Right Mouse Button (RMB) twice , pause, then RMB again) followed by Rebellion's 5 hit attack (RMB x2, pause, RMB x3) that should kill them off quickly.
A Witch will come after you kill enough Stygians, take care of her first before you bother with the rest of the Stygians and they should fall in no time.
Head futher into the corridor and you'll be attacked by 2 Demonic shards, they won't be so hard to deal with since you have the shotgun now.
Go to the next room and you'll be attack by 2 Ghost Rages. Use Aquila's round trip to trap them in a vortex while you deplete their HP with more attacks.
Make your way up to the 106th floor by jumping on top of the meeting room and using Angel lift on the icon.
Follow the arrow into the room and the building will attempt to crush you. Use Angel boost to get out of there quickly.
Make your way to the elevator and you'll be attacked by some Elite Stygians. Kill them off quickly and head to the next room. Be careful of the white holes in the floor. You can fall through them and take damage.
Now head over to the path on the right side you'll notice that the floor is broken and you'll have to jump and use Angel lift to get to the other side. Be careful that you don't fall or else you'll have to fight with more demons.
Once you're on the sky bridge, Vergil will knockout the lasers but fail causing it to turn off and on in certain parts. Wait for the lasers to die and chain a double jump and an Angel boost to get through the upper part of laser.
On the third laser mechanism you'll only have to jump once or else you'll hit the top part of the lasers.
At the middle of the bridge you'll be attacked by a pair of Stygians and a Dreamrunner. Luckily for you the area is small and Dreamrunner is very predictable here. Kill off the Stygians first then take care of the Dreamrunner and proceed to the end of the sky bridge.
Inside the building turn left and you'll find a lost soul hanging on the wall destroy it then head towards the right.
Follow the arrow and you'll find Vergil inside the elevator, head inside and Vergil will give you a new gun.
Take the path on the left and you'll be given a quick tutorial on using Kablooey. Personally I found Kablooey very useless.
Head over to the end of the corridor but don't enter the sky bridge yet. Instead head towards the end and you'll find a lost soul. Kill it then enter the sky bridge.
The sky bridge will fall apart once you get there, quickly run towards the other side and use Angel lift to get there.
Inside floor 154 head into the elevator and it will automatically move to the next floor.
Of course Mundus isn't going to let you in so easily. Some Harpies will spawn. Use Ebony and Ivory to destroy their wings and kill them on the ground or use Angel lift to get airborne and start killing them from there.
After you kill some Harpies a Tyrant will appear. I still recommend taking care of the Harpies first before dealing with the Tyrant. You can use Kablooey on the Tyrant to make it lose its balance and become temporarily incapacitated.
Once the Tyrant is on its knees start attacking its back until it dies.
Drekavac will appear once the Tyrant is dead. This guy is basically the same as Dreamrunner but he deals more damage and is harder to dodge. Although that's probably because the stage is large and his appearance becomes harder to predict.
He's also a lot more aggressive than the common Dreamrunner, he'll attack you a lot so keep your distance to make him use his portal attack and dodge him then land a couple of blows. He'll eventually start deflecting your attacks and you'll have to keep your distance again and repeat the process.
Once you kill Drekavac make your way through the floating stones and towards the core.
Use angel lift on the marks and Dante will automatically smash the crystal and head enter the core.