Now that I finally have Lemmix, it's time to wrap this up with a list of confirmed results rather than guessing based on the Mac version
All the Taxing levels I mentioned as needing testing turn out to be possible, though 8 (which requires 100%) comes down to the last second.
Wild 2 and 10, which I ruled out, are actually possible since both only require 75%. Wild 19 (81%) is only just possible -- you need to free the blocker (or do without one) or you won't make it.
I was right about Wild 11, but it's closer than I thought -- it requires 49/50, which you can get, but the last lemming remains out in the cold! Wild 12 is possible, and 15 is another one that's very close -- you need a lose-4 solution or better.
Havoc 4 is possible with a second to spare, by taking the floor route and building over the tunnel to keep the crowd together. (This is in contrast to the Mac version, where the normal solution to the level finishes in time.)
Havoc 19 fails on DOS; the last lemming (100% required) enters in the last second and cannot possibly reach the exit.
So, here's a complete list for the DOS version. This is a list of
impossible levels, not a list of possible levels as in most of the other challenges
An asterisk indicates that a level is possible on the Mac. Brackets around Mayhem 15 indicate that it's possible on both DOS and Mac, but not Amiga.
Fun - none
Tricky - none
Taxing - 3, 30
Mayhem - 11, (15), 16, 27
Tame - none
Crazy - 5, 8, 10, 12, 17, 18
Wild - 3, 4, 5*, 6, 8, 13, 14, 17, 18
Wicked - 1, 7, 13, 14, 19, 20
Havoc - 1, 11, 12, 13, 14, 17, 19*