Yeah, that's really the main linchpin of this room
From the starting position, get the mimic two squares East of you, and kill the first eye. Remember, you must have entered facing South, so that you and the mimic are always facing opposite ways. Now:
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×Go to the east wall of the chamber, and face East. Step NE. Your sword blocks the mimic, so he doesn't move at all. He is now one square SE of you. Then:
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×Turn to face South. (This is why you have to face opposite ways, to allow this six-step turn without either of you hitting each other.) Step NE again. Your sword blocks the mimic again, and he is now two squares South of you.
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50th Skywatcher