Correct, you need the roach, and it's also important to make the right moves at the very start of the room.
×Enter from the north. Use the time while the roach is killing the first snake to get south of it. Now you can guide the roach inside the NE chamber to kill the second snake.
The snake near the seven orbs is pretty straightforward:
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×Get the roach stuck behind the single orb, then go all the way to the west side, step south so the roach comes out, and run north.
For the snake near the goblin... now the roach is in the third snake's enclosure, that's an excellent starting-point for getting it where you need it. Can you see how?
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×Go to the other side of the middle enclosure, lead the roach east, then west so it gets stuck on the NW arrow. Now enter the NE-most enclosure to lead it north.