Good news!
I've managed to get past the sister fight on my academic play through using two methods: Combat, and trial and error-ing my way through the conversation system.
For combat: This was pretty much a toss of the dice every time and not in my favor. I went in with three baneful dust of Hermes Trismegistus, and Eight Molotov Cocktails.
I had to focus on defense for the first phase, trying to conserve my item resources as much as possible. When the sisters split and start phase two, everyone in the party is healed and at full Sanity and Power, so you simply have to ensure you make it to that point. I used therapy on the academic to keep everyone topped up, guarded as much as possible, and weaved in first aid where I could. Getting past this phase probably had a 90% success rate, so it wasn't too bad.
The second phase is absolutely brutal. I focused on tossing out items for damage, and trying to play whack-a-mole with curing whatever thing was on fire in the moment. Considering if I got lucky they could: Two shot me, Make me go insane with one spell, inflict multiple debuffs, inflict lots of bleeding, I had my work cut out for me. Eventually through pure luck Gabrielle ended up being the only character left alive and sane (as she's the only character in my party with a natural 0% sanity degradation at this point), and somehow survived for three turns alone. She was able to finish off Cassilda with a lucky Cranectomy critical when Cassilda was at 9%.
P.S. Strange Magic is such a good song for this fight, that I streamed it to one of my friends with no-forewarning and she immediately told me to tell you, "I like their music!" It's absolutely criminal if someone stumbles through the conversation successfully and doesn't get to hear it at least once. A lot of the older but thematic music choices for the game are very well done. My compliments for choosing such a wide and interesting variety among investigation A and B that I've heard so far.
For the conversation system: This took me more tries to brute force than you might suspect. Maybe I just had a bad recollection of the choices, but their responses were often not what I expected for everything except the 'authority' option. I'm unsure if the conversation is intended to work this way, but here is how I cleared it in the last couple of turns:
My sequence went something like Compassion -> Intellect -> Compassion -> Intellect -> Intellect. My memory isn't perfect on this, so the order of the first two or three may be swapped.
Near the end of the conversation challenge, I ended up using the Intellect option and asked them who their father was twice. The first time Camilla moved to the left, then after repeating the same thing and hesitating' the bar moved back to the middle and the fight ended.
Besides providing the same question and response as the previous round, I wonder if this was a bug? I'm not sure if it was intended to try the same method of conversation and get the same result twice in a row. If you try doing this at other times it heavily sabotages their attitude toward you.
Overall really enjoyed the fight, and it's probably one of my favorites in the game so far even though it felt *very* difficult. But this was perhaps a symptom of how I built and equipped my party in general.
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In other news I also investigated how things change after doing some of the reincarnations. Going Academic (no Deaths) to Academic after my first death wasn't as brutal with the tips you provided in the other thread, but I did struggle to get enough items to beat the twins and eventually decided to tackle them on a no-death run.
I'm fascinated by what might be behind that force-fielded door in the trio that wasn't there pre-death, and wonder if it will be back later. I assume getting it open has something to do with going insane enough and talking to Vissago. Will definitely try that at some point either on a reincarnation run or a new play through where I let myself skirt into the higher ranks of insanity.
Going academic to occultist at the beginning was a little rough as I felt like I was missing extra sanity. If I I started playing the occultist as my third reincarnation after dying twice on the academic and learning as many mythos spells as possible I'd often have a maximum sanity value in the single digits despite the academic having 30-40 or so before her death. You can imagine how horrible that was. Though I suppose it would provide incentive to try and get to Egypt as fast as possible.
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Speaking of Egypt I tried quite a few of the different rewards (though not all of them). There is an interesting selection of options that will probably benefit people who do a better job of managing their sanity before getting there. Some were kind of underwhelming (like the phylactery). I enjoyed the top-down perspective switch and the transition effects for all of the locations I was able to visit.