So, one of the things I love about the game is how the flipping mechanics can change up a battle, so I wanted to go through the villains available and talk about strategies when it comes to flipping them: Do you want them to flip, when, and why.
I'll do the villains I have, feel free to add your thoughts about them or the others.
Ambuscade: Definitely avoid him flipping -- invincibility and hitting the lowest-HP target can pick off someone if it keeps up. Only reason you want him to flip is so that Haka can eat the darn cloaking device and keep him from flipping again.
Baron Blade: He has to flip for you to win, so the only real issue here is when -- if you're using a lot of deck control to avoid things like Devious Disruption, you might want to avoid finishing his front side off, and forcing his deck to shuffle, right before his turn comes up.
Mad Bomber Blade: You want him to flip as soon as possible -- him targetting the highest HP is preferable to hitting everyone, and the sooner you get him to flip, the fewer ongoing/equipment cards he destroys when he does so.
Omnitron: Given he flips automatically, not much to say here. Just be ready for a surprise on his back side, since you can't predict the second card he'll draw with most deck control.
Cosmic Omnitron: This is a bit of a sadistic choice -- deal with the components or with Cosmitron's direct damage? Smaller games will have less trouble with his flipped side, but generally it's about what poison you want to pick.
Citizen Dawn: Definitely avoid if at all possible. Her being invincible and doing you damage for several rounds can be a game killer, especially if she ends up drawing Blood, Sweat or Tears in the meantime. On the other hand, she can only flip once a game, so in some situations it might help to flip her once, let her flip again and then have full license to wipe out her citizens on sight.
Grand Warlord Voss: For him, it's largely dependent on how many heroes are in the game. In a 5 hero game, you'll usually have enough options to get through his DR (either via boosts or Irreducible damage) that you can leave one relatively harmless minion out and avoid the 3 and 4 HP attacks he'll belt out otherwise (just be careful of the environment targetting the lowest HP target). The equation changes in a 3-hero game, however. With DR on your side, you can more or less ignore his attacks and take him on directly, so you'll want to flip him quickly, and keep him flipped.
The Chairman: He's another one you have to flip to beat, so again it's about timing -- he buffs his thugs and does retaliation on attacking, so you might want to keep him from flipping until after the Operative is out of the picture and the Contract and his gunmen are taken care of.
The Matriarch: Definitely one to avoid, as her healing on the fowl cards can boost her by something like 20 HP in a single turn if you're not lucky. If she must flip, see what you can do about deck control and field control -- one of the luckiest flips of hers I had, Huginn and Muninn were on the table with low HP, she played a Fowl card, shuffled her deck, then Darken the Skies -- which did nothing, thanks to a now-empty trash. With the Cohorts still out, killing them kept them out of play the rest of the game.
Spite: This one is complicated, because of the role the drugs play. In a 3-hero game, his drugs have much less impact, so you're more or less safe letting them come out (with the possible exception of PL626 Compound XI, if you can't reduce his damage). In a 5-hero game, however, you want to avoid his drugs -- and him flipping -- as much as possible because 3 DR can be horrendous for low-damage heroes and putting 3 ongoings/equipments back in hand every turn can kill set-up. When he flips, it turns into a straight damage race, so you might want him to flip early so you can just pound him without worrying about his healing. But really, the best time for him to flip is when you've got a ton of Victims in the safe-house.
Agent of Gloom Spite: Flip as soon as possible. The fewer drugs he has face up, the better. If you're really lucky, he'll flip with only one card up that you can easily deal with. Otherwise, like with regular spite, smaller games have it a little easier.
Plague Rat: Here it depends on how well you're managing the Infections. If you've got, say, Ra on the team and you can make yourself immune to self-damage, you can use his flipped side as a few rounds of healing. Doubly so if you can put a Twist the Ether on him. Otherwise, the best use of Plague Rat's flipped side is clearing the table of Infection cards without penalty -- and with them in the trash, it takes a lot of bite out of his one-shot cards.
Akash'Bhuta: Letting her flip can make things easier and more predictable -- since she plays cards on environment target destruction, you don't have to worry about a surprise in the Environment's turn pulling out Entomb or something when you're not expecting it. So, by all means, let her flip as soon as she can.
Apostate: For the most part, avoid a flip, because him targetting the lowest-HP target and healing just isn't good for you. The main exception would be if Orb of Delerium, Runes of Malediction and Tome of the Unknowable are all out and you don't have enough damage to overcome it -- then letting him flip might be the only way to get that card out of the way. Otherwise, just focus on taking out the relics as you whittle down his health and try to time it right.
Gloomweaver: There's no good reason to let this guy flip. He heals, he starts doing direct damage (dangerously so, if you haven't taken care of the pins), and you lose the instant-win option.
Skinwalker Gloomweaver: You have to flip him to win, just be ready for it -- he'll be attacking for huge damage on each of his turns, so make sure you can mitigate it before he does with Hypersonic Assault or Throat Jabs, or Twist the Ether and Flesh of the Sun God shenanigans. The one bit of good news is he'll keep his own cultists and zombies in line and take some of their heat off you, and he will no longer get any benefit from Strength of the Grave or the Pouch of Bones.
The Ennead: Technically you have to make them flip to win, but the order can make a huge difference. You definitely want to avoid their rules card flipping if at all possible (and on Advanced, it usually is not), as it will typically mean lots of healing for them (up to 3+the other flipped effects and card reactions), and it means you have a lot to deal with.
Individually, it depends on the heroes involved, but in alphabetical order:
Atum: Shuffling the villain trash doesn't do much, unless you're dependent on Wraith or Visionary's deck control. Otherwise, I take him out quickly to avoid the extra card play he's prone to.
Geb: Unless you're playing someone like DW Nightmist or you're waiting on the card that AA or Tempest just fed you from your trash, there's little difference made here. Usually safe to let him flip early.
Isis: Depends on the hero -- Tachyon loves having more cards in the trash (though not so much when it forces a reshuffle), and if you've got Mr. Fixer on the team, a quick trip to the junkyard can fill your hands with everything you need after a round or two of Isis flipped.
Nephthys: Pretty straightforward, while healing the badguys isn't good for you, 1 hp a round isn't going to break anything, either.
Nuit: With the exception of Silver Gulch, reshuffling the Environment deck is about as painless as it gets. That and the fact that Nuit gives the rest of her team DR makes her a good first target.
Osiris: You don't want to discard, and you don't want to do yourself damage (especially if you've been buffing), so you want to take him out. Plus, if you're in a target-heavy environment, he can keep that deck in check for you. Captain Cosmic and Unity, however, don't like him flipped so much, so they should be prepared to lose a bot when this happens.
Set: While the villains playing an extra card can be rough on you, every player getting a free play is more than worth it. I've had games won entirely because Set pulled out damaging one-shots for the hero team one right after the other. Combined with a Take Down or Mistbound? It's like Christmas.
Shu: Another one who's largely harmless, given how many Environment cards only act at the end of the Environment's turn. So long as he doesn't play Lost in the Past immediately before Nuit's incapacitated side, you'll have plenty of time to deal with whatever environment card pops up.
Tefnut: Discarding a card every round can be a pain, so I tend to keep her on the field until I'm ready to end the game. It's not so bad in the late game, if you've had time to stock up your hand, but losing options is always rough.