The general idea is to have the soldier help you kill the aumtlich in each chamber by either distracting them while you kill them or killing them while you distract them/freeze them with your sword. There are apparently multiple ways of doing this, but here's what I did in my demo:
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×May as well take the speed potion first. Then I dropped the middle bridge first then the north bridge second, leaving only the southern bridge for the soldier to enter on.
I took the soldier potion while facing west so that the soldier would get frozen by an aumtlich fairly early on in the the room. This allowed me to run down and be close enough to distract the aumtlich at (5,18) and then freeze it in place by reflecting its beam. With that done, the soldier was able to make his way into the southern alcove and we took out the aumtlich there together. I did two while he was standing on the plate and he did the last one (mostly I let him to this to get him off the plate.)
The other two alcoves were pretty similar. Let me know if you need more specific details. The room is pretty chaotic so a lot of the difficulty for me was just overcoming decision paralysis and trying something out to see if it worked.
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Links to neat forum tools that I always have trouble finding:
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