We all saw this coming the moment Vergil opened his mouth and commented coldly on Kat.
Equip the shotgun at the very beginning of the battle and start shooting at Vergil. Much like the Dreamrunners, Vergil will also deflect all your attacks including gun attacks, but the shotgun quickly destroys his spectral knives.
Slowly make your way towards Vergil while shooting at him. When you get close enough start attacking him with Rebellion and he'll counter you.
Dodge his attack and he'll be vulnerable for a while. The easiest attack to dodge is the one where he teleports to the air and attempts to attack you. Dodge it then start slashing at him.
After you deplete his HP enough Vergil will now summon 4 spectral Knives and will also have a new attack. You can take care of the spectral knives the same way regardless of how many he summons. Get close to him while shooting at him with the Shotgun then attack him again once you get close enough.
Dodge him as he gets into attacking position and retaliate with attacks of your own.
Sometimes he'll be too far from you after you dodge his attack and you won't make it in time to attack him with your sword. If this happens just shoot him with your shotgun and get closer to him. If you're too far then at least you damaged him a bit but if you're at mid range then you might make it in time to land a couple of hits with your sword.
He'll be a lot faster after the second short cut scene and he'll have more attacks. But unfortunately the battle will still play the same way. Just dodge him and get some hit in.
Once the scene starts getting darker and lightning starts shattering the sounds things will get serious. It'll be a bit hard to dodge some of Vergil's attacks now the quick slashes in particular are hard to dodge. You may need to jump to avoid it. Second is his charged attack in which it acts like Aquila. It's easy to dodge though just move out of the way and you'll remain unharmed since the range is very small.
The best way to land hits on Vergil during this is to start shooting at him whenever he finishes an attack or while he's in the air. You won't be putting in much hits with the Rebellion at this part of the battle since he'll recover a lot faster after an attack and he'll also attack you with quicker blows.
Once you damage him enough he'll summon a spectral version of himself. This is sort of like Vergil's Devil Trigger. His attack pattern will stay the same except now you'll have to watch out for the two of them.
Always keep both of them within your cameras range. This is the best way for you to avoid his attacks and not get hit by either one.
Vergil and his clone will, however, attack you at the same place. This makes it easier to damage him as Dante won't get distracted by the clone if it's closer.
Vergil will also favor his aerial long range attack now. This makes it a whole lot easier to damage him as you only need to dodge the attack then start shooting at him and dodge another attack and shoot him. Don't worry if you're not putting in any hits with your sword. It really gets hard to get close to him at this stage.
After a while the clone will start acting independently. Vergil may attack you with a different attack or dodge your attack while the clone attacks you.
Keep on dodging his attacks then shooting at him and eventually Vergil's clone will disappear and you'll be able to take him on with your sword again.
After you get his HP down to the last bar the clone will re-appear again and defend the fallen Vergil. At this point you won't be able to damage Vergil anymore.
Once this happens go into Devil Trigger mode and the clone will disappear. Land your final blow on Vergil to finish the battle.
Now sit back and watch the finale. Congrats! :)
One last note though, remember those places you couldn't reach before because you didn't have the necessary weapon or ability? You can replay the game and all your skills and weapons will be available. Have fun getting the completions. :)