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Okej, for future reference, here's the strategy on nightmare mode that eventually worked for me:

(first thing is what Aura does, second thing is what Slimey does)

(this is with nasty weapon coating on, unsure if it's necessary)

Turn 1:  Heat Up, attack phantom.

Turn 2:  Heat Up, attack phantom.

Turn 3:  Light I on phantom, attack phantom.  Lamia will switch to Offensive Stance.

Turn 4:  Attack Lamia, throw Flash Bomb.  The attack on Lamia should do roughly 500-550 damage.  (The flash bomb isn't strictly necessary but makes the RNG for the remaining steps less hellish - the Lamia needs to NOT hit Aura, and Slimey won't last long enough if she hits every time)

Turn 5:  Heat Up, Protect (or defend if you're feeling lucky and want to leave it to RNG whether Lamia attacks Slimey or Aura, with the benefit that Slimey would survive at least one hit).

Turn 6:  Light I on Lamia, Protect (or defend, etc)

Turn 7:  Rampage I on Lamia, and what slimey doesn't doesn't matter because either this will finish off the Lamia (dealing 1500ish damage), or it won't (because the Lamia randomly used guard or because you missed due to RNG) in which case you have to reload

In any circumstance, the Lamia choosing to attack Aura is basically instant death.  It spends the first four turns powering up, but after that it's basically RNG whether it chooses to attack Aura or Slimey (or, sometimes, it randomly guards for seemingly no reason).  If you deal enough damage (I think about half health), it will summon its snake friends, which is also basically instant death.  Do NOT use Offensive Stance as the pure run walkthrough suggests, as it doesn't work here (you can do steps 1-4 if the phantoms randomly choose to not attack Aura, but if you attack the Lamia with double-boosted attack with tactical advatange, it deals around 1000 damage, which isn't enough to finish off the lamia but does bring it below the point where it summons its friends).