All right, so some setup:
-Devil Trigger (Dante, Vergil, and Nero) is restricted to 2 a day to to the nature of it requiring absorbing a lot of demonic energy.
-Bigger moves/abilities like Judgement Cut, Quicksilver, etc. is 3 a day
-Trish's lightning and Nero's "mage hand" are cantripts, so unlimited use, because of the nature of their characters and their gameplay connections
-Because they all hunt demons, pretty much all their weapons are already magical.
-Because everyone's faster than any of the fighters in here, it'll be treated as having extremely high Dexterity. Not impossible to hit, but still extremely difficult
Floor 1: This floor is child's play for them. None of the baddies can actually hurt them and everyone resists the magic the Ogre can throw at them. Even the Carrion Crawlers can't paralyze them, they've fought enemies like them and weren't affected. Dante would probably take the +1 weapon since that's his schtick. I'm going to assume it turns into shotgun-nunchucks since that's funny to me.
Floor 2: While the monsters still can't really hurt them, the resistances make it a bit more bothersome. They all have NPI and Vergil can shake off illusions, so he can make those who can't tell aware or get the casters from a distance with his sword beams. Dante will probably keep the gem since he's the collector and it's backup just in case something happens to Vergil.
Floor 3: If all of the Kuo-Toa attack at the same time, then the in character move for them would probably be either Dante slowing down time with Quicksilver and picking them off or Vergil doing
this and oneshotting them all. The Cambion may cause some trouble since they're all only immune to one type of corruption, but considering they fight demons like that regularly, it'll probably go down pretty quickly. Again, Dante gets the gem for later. Considering he basically turns demon souls into weapons, he may do just that, but that's purely flavor.
Floor 4: This is where things start to get difficult. The devils, Horned excluded, aren't too much of a problem, the DMC heavy hitters resists most everything they can throw at them and aren't really hurt by them. The dopplegangers are in trouble since most of them have no friends or it'd be obvious that the person shouldn't be there. The Horned Devil may be difficult for Dante and Neuro, but Trish and Nero would have less trouble. Devil Trigger may be used here by at least Dante or it'll turn into a range game with their guns and magic. Soth is the main problem. Vergil can find the wall he's hiding behind, but Power Word Death could get one of them dead, most likely Vergil. It'll take some heavy lifting on Trish and Neuro's part, but they can clear this floor. They may use their wish to bring the fallen back to life so they can fight the final room at full power.
Floor 5: Going through each BBEG one at a time.
Vargo would get rid of Trish's magic and his magic would be difficult to get around, but once they get in close, the swordsmen can cut him to shreds. The familiar will probably be bothersome, but can be dealt with relatively easily.
Aerisli would be easier than Vargo since her magic is more limited. Sure, the legendary resistances would be extremely annoying, but Spear Bird Lady would be brought down.
Vladmir is even easier since he has much less magical and is another big swordsman they can either gang up on or keep at range with guns. Since they have NPI and Soul Manip, his soul form can be destroyed.
Elder Brain will be hard. While they normally resist Madness Manipulation, it's not the type Elder Brain uses, so they may start taking mental anguish. If they can kill it before that spell is used, maybe they'll be fine. If the Brain sends someone to another dimension, Vergil will have to waste a Judgement Cut to get them back. Devil Trigger will most likely be used here by at least two of them.
Drizzt is easy, just a swordsman with various elemental stuff, basically Dante. If they're mentally disturbed during this fight, it'll be slightly more difficult, but it should still be relatively easy.
Soneillon is going to be very hard. While her magic type is similar to the devils earlier, her Regenerationn will be very difficult to get past. They'll have to time beating her physical body and then destroying her soul, probably involving Yamato's spatial manipulation. Either that or they banish her with Judgement Cut. If they get a string of bad luck, Dante and Vergil may die.
So overall, best case scenario, they clear the dungeon alive but mentally scarred. Worst case scenario, Dante and Vergil don't make it out. Overall, DMC should have the hax and skill to make it through the dungeon in some capacity.