One important thing to note is that you should start backing away early enough so that the goblin is in position when you move out of their range. You can also try to position a goblin a few diagonal squares away from the position you want in order to make it easier to get additional goblins into position (and once the earlier one(s) are back in range they will go to the right square).
A few more hints follow, though this room is mostly figuring out how to execute your strategy:
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×You'll probably need or want to bring more than goblin with you at the same time at least once.
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×It's possible to get all the goblins you need on the tiled path, but...
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× ...you have a lot of vertical space to work with in the mimic room. As long as the goblins are in the correct horizontal position you'll probably be able to reach them.
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aka VioletPumpkin