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Basilisk Kotone: 

You need to get through about half of the sky dungeon, if you check in on Kotone regularly you will see a Basilisk has entered the prison room as well. They will be right next to you, so do not move when you enter the room to check.
If you see the Basilisk, their back will be to you, and they will approach Kotone, let the scene play out.

Kotone Aelo: It is simple, lose the boss fight in the sky dungeon, I don't know if winning the mini-game is part of it but if you lose you get a mini-game animation.

You need to get grabbed by 3 Basilisks.

Does anyone know how to get this scene? This is the Nyx storyline and I feel like aside from working my way through the Scavenger place I have found almost everything, unless it is two Incuflies.
EDIT: Just tested the Incufly thing, there is no double grab animation like the undead or others so that is out of the picture.

Apparently it won't show the picture, the scene between "Incufly" and "Kappa" is still not found in Nyx's playthrough

You may have figured it out by now, but you need to get the dragon plant to shoot a fireball at the red blocks, if you jump and attack at the right time, it won't hit you.