Vergil is the final boss of Nero / Dante / V route which is encountered in Mission 19 as Dante then 20 as Nero.
Dante
This fight is RNG heavy due to Red Hot Night setup. You also must equip DSD during second phase of full charge for Sword Formation: Round Trips stun after he gets hit by the meteor.
Do not DT until Dante is close to the final charge or about to get hit by Vergil's Rapid Slash and such.
If you get hit by PS and knocked away by his Judgement Cut restart checkpoint to re-do the setup.
If Vergil dodges Red Hot Night then use RG actions to kill or counter him with Cav Air Combo B
NG+ Faustless is must more consistent fight because you can setup the same behaviour against Vergil with Kalina Ann shot. The cycle will always be Air Combo B → Cayote-A JC → Air Combo B → Release → Air Combo B
Nero
Scripted fight in both settings with different setup up.
Optimally, you want to have JC avaliable however, its difficult to make that decision most of the time. The reps of Aerial Combo depends on the Bringer Claw hits and Exceeds.
Buster has to be done in DT for more damage. Keep in mind that Nero DT-rate consumption is high.
NG must do iFrames against Vergil'sAerial Cleave before launching him into Roulette Spin → Aerial Combo → Blue Rose then approach him to counter his next attack with High Shots → Snatch → Aerial Combo. From that point finish him off with good DT reps of Aerial Combo → Buster