I've fought everyone at least a couple times now, so I'll give my impressions.
Ambuscade - Relatively straightforward boss who wouldn't have been out of place in Vengeance, followed by the craziest incap ability of any villain. Dealing with a mini-nemesis boss rush can hurt, and God help you if you let Ambuscade live long enough to reshuffle his deck.
Biomancer - Hate this guy. His damage reduction and healing mean that he's hard to kill even with his low max HP, his homunculi have damage reduction making them a pain to devote resources to, and so they'll be hitting everyone pretty consistently. Then you have his hero clones, which are almost always must-kill targets, and then a card to bring them all back from his trash pile. That one's more fair than most, since you can destroy it, but you might not have much time depending on where he falls in the turn order.
Bugbear - Mostly a beefy damage dealer, not unlike Fright Train. He does a bit less damage than Fright Train in general, at least until the body count starts racking up, but is much sturdier thanks to his lifedrain. Makes for an interesting decision; do you wait before taking him out so that you don't have to deal with his healing until later, or do you target him early so that you can avoid his insane damage in the lategame?
Citizens Hammer and Anvil - Between these two and Anvil's starting equipment (which is almost always a priority target), you have something like 45 health to punch through, and it has to be in a certain order. That's not taking into account the chance that Anvil pulls one or two Bastions to make things more of a pain. Their damage isn't too high, but Bastion means that you'll often have to focus on Anvil before anything else. Basically, they're the party tank.
Greazer - Would probably be one of the most dangerous villains of the bunch if he wasn't so single-minded. He leaves once he's incapacitated his target, and even though his incap ability is a strong one, it's sometimes the right move to let him get his target just to get rid of him. Also, he has one of the funniest interactions in the game: if you can use an ability to make his hair do damage to itself, Greazer will respond first by counterattacking his hair, and then counterattacking himself for damaging his own hair.
La Capitan - A support character for the villains, her deck's not very threatening but she has a few discard effects (and she becomes more dangerous paired with someone like Ermine for even more discard), and some weirdness like switching a hero's ongoing for another random one, taking extra turns, or letting the environment take extra turns. Also, took me some time to figure out who the woman on the back of her character card was.
Miss Information - Also a support character, she has some dangerous ongoings, and she can make the earlygame surprisingly difficult considering that she's supposed to be a difficulty 1 villain. She's probably harder than La Capitan, honestly, and will probably be one of the first villains targeted in a match. It helps that her incapacitiated side is beneficial for the heroes, at least as long is she isn't on La Capitan's team.
The Operative - She does damage, and has a couple random debilitating effects. That's about it, really, aside from the rare game where Iaido Practitioner actually does something. I was pretty disappointed with her, to be honest, considering that she's half of the villain generally seen as the most nightmarishly difficult in the game.
Plague Rat - Kind of the opposite of the Operative for me, I'm not a fan of his normal fight, but as a member of a villain team, he's a blast to face off with. Most of this owes to the Ghostbusters, who provide an interesting dynamic for the fight. They're pretty dangerous, but they're also the only things keeping Plague Rat in check, as without them, he can do as much as 7 damage to a character with a one-shot, plus 3 to everyone at the end of the turn. 10 damage to a character is a lot for a Vengeance villain. But on the other hand, without the busters around, Plague Rat can also help you take down the other villains, not to mention himself. Very interesting decision-making here. His incapacitated side can also be a life-saver, destroying pesky environment targets.
Sergeant Steel - A nice way to tone down the expected tedium of upkeep for a mook-maker villain in the Vengeance format, it's nice that only one of his minions will act at the end of his turns. On the other hand, they're still very dangerous, and beating them will feel fruitless as it just means that a different one will act at the end of the turn instead. He also has low health, so, you know: kill him fast.
While I'm posting this wall of text, might as well talk environments, too.
Magmaria - A lot more than the "lava burns everyone all the time" place than I thought it would be, it has something of a currency system where you can destroy some environment cards, keep them, and trade them for bonuses later. A system that I'm sure would be really cool if I ever drew those payoff cards before the end of the game.
Court of Blood - Vampires beat people up. It's a very straightforward environment; but it feels quite fair. I like it as far as gameplay goes, even if the accents in the flavor text make me cringe internally.
Zhu Long's Temple - Probably benefits the heroes even more than Freedom Tower does, and wouldn't surprise me if it ended up being considered the easiest environment in the game after all was said and done. There's only one card that's uniequivically more help to the villains, and any environment destruction can just be saved for that one card. It's a fun environment, though, and I recently noticed that the True Form isn't just the Fixer's nemesis - he also counts as the Operative's nemesis, which allowed him to hit her for 12 damage in a single turn.
Fantastical Festival - A little too much going on for my tastes. Can get very out of hand, very fast, with no inherent ways of getting rid of many of its cards.
Celestial Tribunal - Not technically part of the expansion, I know, but oh my God this place is so cool! Personally, I like to let the randomizer choose which character to take out of the box as the Representative of Earth, to avoid just picking the obviously powerful ones like Legacy, Team Leader Tachyon, or Captain Cosmic every time. Though sometimes this means you'll get a useless one like the Naturalist, Absolute Zero, or Prime Warden Cosmic.
Overall, Villains of the Multiverse might be one of my favorite expansions. I wasn't actually that excited for it for a while, since it had no new heroes and I rarely played the Vengeance format, but what I found was this: The Vengeful Five, on their own, were basically a single villain with a few extra bells and whistles. But adding the ten new mini-villains really makes the Vengeance format feel like a brand new game.