Oh, the Hospital one was the second one I got, I was trying to get needle boy and blood clot boy, and this popped up out of nowhere after I finished 2-12X Grey Matter.
Ok, either dark worlds are indeed also necessary for these achievements, or this is really, REALLY strange coincidence. I just finished said level again, 2-12x. I didn't even try hard, as my old record there was kinda week (must've been set in the first few weeks of my playtime), but now I got it.
I don't even know what to say, because this is incredibly confusing. Thank you very much! :)