This room was a rough one.
The main trouble spots are the two roaches.
In general, you can easily kill a snake by dropping the trapdoor on one side of it, which will make the monster easier to manipulate. But the roaches are trickier, as there are force arrows that interfere with the brain pathmap.
The west roach should be handled first.
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×There's more than one crumbly wall near the spot where you have to place the mimic. I didn't notice this at first. You want to get the mimic over in that area so you can use its sword to stop the roach from going north. Obviously, this has to be done before you can hit the orb with it.
This takes a little dancing, but isn't that complicated. Just be sure you don't move too far to the right in the process; you want to keep the eastern tar baby from going past the closed door.
The east roach is trickier.
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×You need the help of the east tar baby. You need to keep it southeast of the door, then lure it northwest through it.
But there's more to it than that.
Do NOT drop a trapdoor for luring purposes on the second snake from the east. You need both trapdoors intact, one to get in and one to get out. You can still lure the tar baby in to kill this one; I think it's easier because of the direction the snake is moving in.
So, once the tar baby is in position, stand on the east trapdoor to block it, let it kill the snake, kill the baby, and head in. Step on the force arrow so the roach sees a path to you. Once it's far enough up to manipulate, go back through the other trapdoor.
Now just manipulate the roach to the fifth serpent through the usual tactics.