This is a pretty tough room, there are several things to do here.
Increasing hints:
Click here to view the secret text
× The main point in this room is that in both timeline all monsters must be killed, otherwise you can't exit the room. The big problem, on the other hand, is that the two timelines are strongly depending on each other. Here's some hints on both timelines.
Click here to view the secret text
× Timeline 1: lemming behind black doors is not a problem, you can let him free and kill it outside, in the second timeline he will not press the pp. The bent-tail lemming however is quite important though, because it's the last monster that needs to die, in both timelines.
Click here to view the secret text
× Timeline 2: well, first thing to do is prevent the lemming behind black doors and bent-tail lemming from stepping on the plate. In the end you'll have to go to (2,8) and just wait, this can only mean one thing...
Click here to view the secret text
× ...it means that at some point you need to manipulate the bent-tail lemming so that timeline 1 doesn't desync, so you'll see again what you did. After that your job is done.
Click here to view the secret text
× Note that I didn't mention red doors at all, but I left a subtle hint on when to deal with them. Also, keep in mind that the pp from (20,7) to (20,15) is the big deal, that's the one you don't want to be pressed.
____________________________
There's not some other world out there where everything's gonna be okay.
There's just this one, just this rock.
-33th Skywatcher