In Yellow Ether Floors you spawn on a plattform with yellow ether around it and you have a timer during which you need to shoot down as many as you can.
They seem to be very rare. I have gotten only one in my current 100 floor run. In this thread [forum.psnprofiles.com] people are asking the same question and one user theorises that running only 1 to 30 runs is the best way of farming those.

Thanks for this! I've managed to find all the cats, but still have a few more Yokai to go...once I've found them I'll try just running floors 1-30 and hope I can find 5...

Running 1-30 seems to be slightly quicker. I found one when going to Floor 185 to get all cats. Then used the thread to reload any floors 1-30 for specific Yokai, and got a couple of yellow ether floors on the way. I got them at 10 and 28 on one run, 10 on the next, and then tried reloading 10 a lot and didn't get anything on the third run. It seems like it maybe has a chance if you just don't pick anything up? So if anyone else is struggling with this then maybe re-running 1-30 and just avoiding everything will help for you as well.

It took me around 900 floor (retrying often). The highest floor you go doesn't affect the chance for it to spawn.

i got like 1 over 400 floor, and then i got 2 in less than 10 floor.

I completed all others job first, then i was just rushing from a floor to an other as fast as possible to make them spawn.

It seems to be entirely random. I have 4 yellow ether rooms and the only other tasks I'm missing are 2 of the cats and one more yokai encounter (the hopping umbrella one).

It took me 333 floors to visit 5 ether floors.

I'm on floor 149 after 2 30 runs and I have yet to see 1 this is ridiculous