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I assume that you drop the trapdoors right after a spawn would take place.

It helps to leave the northmost trapdoor for last, as it gives you the most time. If you do this, you should have enough moves to kill the two queens on the west wall before a spawn takes place. If you can do this, there will only be 18 roaches spawned each spawn cycle, which should give you plenty of room to pick off the rest of them.

As far as general technique, brained roaches tend to be easier to kill by side-stepping rather than sword-swinging. you will probably have to do some experimentation to get this part. You might also try experimenting a bit in Golem Gulch: 1W if you want to hone your brained roach technique (although, of course, the solution there is much different). As I look through the hold, this is the first room where you really have to deal with brained roach hordes in an open space.

It's doable, though -- let me know if anything I've offered here is useful.