There's 2 major things I did:
1. Reset until you have Ligeska as a student pred with you (assuming you beat Ligeska's regular map already). When Ligeska is swallowed by Satie, Satie is unable to swallow anyone else, letting you do what you want for a short time. Keep in mind you have to be aware of if Ligeska is either spit out (a distinct audio cue) or instead digested.
As a result, if you explore where Ligeska is going, you'll be safe, as long as you make sure Satie sees her first.
2. Utilize key dropping. Find a room you can hide in (classroom, bathroom, etc.), stand outside it and drop a key.
If Satie doesn't come running, you know she isn't around and you're generally safe. You can run around, explore, and open doors.
If she DOES come running, go hide in the room. She'll run up to the source of the noise (the key), then be on her way. This lets you keep track of her location to proceed accordingly.
Just stay patient. Hope this helps.
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I managed to do it, almost didn't make it at one point. I had the exit key, but got caught on the middle floor as I was making my way to the exit, I got lucky and got out, and waited for the key so I could finally beat that nightmare. She ended up bringing it down to the kitchen floor in the cafeteria, and after a bit of time passed and I got the exit key again, I went back up to the middle floor. I saw Satie chasing another student that somehow made it that far, so I was able to gun it for the exit. I never want to do that again. At least for today.
I've tried her nightmare few times now. Ligeska has a slower 'neutral' speed, but like all predators, she can outrun you on an empty stomach. You can use the other 2 students as bait, but she'll STILL chase you, and she'll digest her prey quickly.
Her being silent and excellent at hunting prey makes it difficult, it's been harder than Satie's nightmare for me