I can't picture the screen in my head at the moment so I'm not 100% sure this will work. Try throwing the grenade from the previous screen so that it lands on the other side of the slig. Wait until half a second before it explodes and step to the next screen. If you've judged the moment right, the grenade should blow up before the slig can react to you and if you've positioned it right, it will blow up the slig and not you.
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Spending as long as I do here, it's easy to forget that Oddworld has actual fans.
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