You only really need the top queen to spawn once before you kill her,
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×and use the roach egg to give your mimic an extra boost.
If you can't get that to work,
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×flooding the room with roaches (after you place the mimics in both rooms) works great, but takes a long time.
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×Making the mimic 'dive' into the roach horde will ensure that you can make it surrounded on all sides by roaches, giving you plenty of opportunities to offset its movments.
Of course, it's also possible to kill all the roaches in the top chamber without letting the queen spawn at all, which is the fastest way, but it's pretty tricky.
Oh, and be careful when walking on the trap doors. You want to make sure you have a path out. Thankfully, there's no red door, although this room would still be solvable if there were...