The guard is impossible to kill, however if you can raise the green door before the bomb next to it goes off, the guard will not count as a monster. So that's really the main puzzle of the room, to have the Evil Eye be the last monster killed.
First thing you might try is to kill all of the other monsters as quickly as possible although this might prove to be hard because
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×the fuse is too short. Can you think of any other way to delay the burning of the fuse?
Further hint:
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×What if you could stop it burning completely?
Solution Spoiler:
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×Put one of the mirrors on the fuse, this puts the fuse out! Now you have all the time you need to kill the other monsters.