On my 83rd attempt, after nearly 2 hours...
Yeah, I finally beat Yuugi and then Suwako on my first try. I've also managed to beat Nue's alt spellcard three times now, and I find it easier than her normal one. Nowadays I can get to Nue's phase 4 in about 5 minutes!
Some tips and strategies (Lunatic):
For learning a new part of the fight, using the spellcard (Temperament: State of Enlightenment) that grants extra damage, defense, and super armor is the way to go. It'll allow you to make mistakes if you need to, and is overall more useful than the measly damage that the other spellcards can output. Using 5 bars of scarlet power isn't bad, and leaves you with 4. Eventually you'll get back up to 5 and be able to use it again if needed.
I like to use the headbutt and Ballista whenever possible. The charged headbutt does a lot of damage to both health and amulet, and is easy to execute after 2x slash. The ballista has excellent range, does decent damage to both health and amulet.
Nue has the hardest difficulty curve so far, IMO. I like to use Ballista and Non-Conc. Detonation to clear out the snakes. The detonation doesn't cost much power, is a small aoe, and kills the snakes in one hit. If you time it correctly, aim the ballista and shoot right when Nue releases the snakes. It should kill 2-3 of them right there. Finish the rest with detonation, OR let Nue attempt to melee you. If she does melee you, dodge upwards, do a downward slash to activate the weather, then charged headbutt, down slash again, headbutt, and that should break her amulet.
Phase 2, dodge her bullets to the left or right once, then wait about a second or two, and dodge to the side again. Once she comes out, slash, charged arial side attack, slash, and then headbutt. That'll break her amulet and pretty much end the phase.
Phase 3, almost the same as phase 1. If you let her use her rain attacks, make sure you clear out the snakes, go to either sides of the stage, dodge up, land on the floor, and dodge up again.
Phase 4, now this is probably the hardest phase to learn. Use super armor right as you see Nue coming down. That'll prevent you from getting killed in two hits and allows for much more leniency. It's hard to describe what to do, but the best thing I can tell you is just to chase after Nue and make sure to dodge to the sides in the air, to get her bow to quickly move to the side. Sometimes when I am lucky, I hit Nue with her first bow attack and then the second hit comes shortly after.
Phase 5 normal, Bonten Grenade to help with the UFOs, and Detonation for the snakes. Either use super armor to learn this fight, or Scarlet Weather Rhapsody of All Humankind to finish Nue off when she has about 1/3 health left. Always clear out the UFOs and snakes before going for Nue. One slash will kill the UFOs, but it's best to dodge and then attack then as they REALLY hurt. The longer you take, the faster they start spawning.
Phase 5 alt, stay near the left or right edge, and bait Nue into using her Snake/laser attacks then run or dodge to the edge of the screen and start slashing away. Rinse and repeat. Getting hit by her melee results in her using the rain attack. If you trigger her rain attack, the middle is probably the safest place to dodge upwards but be aware that she will sometimes jump onto you in the middle. It only really takes a few attempts to learn her moves. No spellcards necessary, but super armor is always useful and Scarlet Weather Rhapsody can finish her off.
Edit: seems like she only does her rain attack if she gets a melee attack off on you during her alt 5.
Yuugi is much easier than learning Nue, but it's a long fight and patience is required. NEVER attack Yuugi head-on, always dodge and counter-attack. She actually attempts to dodge your ranged attacks during phases 1 and 4, but during phase 2 and 5 I highly recommend using Ballista.
Phase 1, let her come towards you, dodge, 2x slash, headbutt, run away, repeat.
Phase 2, Dodge into her fire, double slash, headbutt, dodge downwards, repeat. Ballista when you get the chance. Don't get greedy with the slashes or else you'll get hit by the fire.
Phase 3, Dodge into her when she shoots out the fire. 2x slash, headbutt, charged down attack (with the earth thing at the end). When she hits the fire to shoot out smaller orbs, the best place to be is away from the center point. Once the orbs are out, she will come towards you and try to attack you. Just dodge, and use that chance to damage her as much as you can with 2x slash and headbutts before she repeats.
Phase 4, Same as phase 1 but with the addition of being careful of the rocks.
Phase 5 normal, Same as phase 1 and 4, but without the use of headbutts. It takes a lot of patience, as Yuugi has a lot of health and 2x slash doesn't do that much damage to her. However... she will NOT dodge the ballista, so use that whenever possible. If she punts you into the arial bullets, dodge downwards.
Phase 5 alt, I managed to get her here once and took her down to 33%. I used super armor at the start and just dodged her attacks. Sorry I don't remember too much. I think I may have been able to bet her if I used super armor again instead of wasting my scarlet power on a Peerless Blade, which barely did any damage to her.
Let's see... As for Suwako phase 1, this time the tail of her rock snake shoots out bullets and her other attacks shoot out more bullets. She can also curse you (slower orb regen). Be VERY patient and only attempt when given the chance.
Phase 2... Dodge her rings and curses, attack when given the chance, and use ballista.
Phase 3... is her big golem I think. First she starts off by shooting out a curse ring. Just dodge that and go straight for attacking Suwako in the center. I think in normal mode, she sometimes shoots out one lightning orb. In lunatic, she shoots out three or four. Just dodge and go back to hitting Suwako. Rinse and repeat. Her attacks don't do too much damage.
Phase 4 is actually really easy. Just avoid Suwako, use Ballista, and she'll end up giving you lots of free scarlet power to keep on Ballistaing her. Your only real chance at slashing her is when she uses her cone attack. Overall, I feel like Suwako is easier than Yuugi.
When I got to Iku, I basically got killed by her before I could even get an attack off. Her lightning attacks now cover a larger part from the ground up.
I hope some of this information helps you guys. Now that I can beat Nue more consistently, I'll be working on trying to beat Yuugi consistently. Perhaps I'll get that down by my 100th attempt... Good luck!