I've tried Taxing 21 again. I /nearly/ came up with a 6 skill solution, but it just barely doesn't work. By making a second lemming a climber, and having him take over the rest of the work (but this both uses a 7th skill and fails to get 100%), it will work. Maybe someone who knows more could improve on it?
Basically, it involves the dig-the-side-of-steel glitch to get past the flamethrower... and from there the rest is obvious.
I've already considered this since I was the one to issue the no-builder challenge for that level back on the old old forums. I don't think you can get that to work with less than 8 skills actually:
1) You need to dig down the edge of the steel block a total of 12 pixels. Then because the initial frame of falling goes down 4 pixels, the lemming will "fall through" the trigger area skipping it in effect.
2) I think you need at least 3 skills to clear away the top 7 rows of pixels of steel: build twice to the right height and bash, or climb dig bash.
3) You then need to set up a blocker to enable you to dig down the final 5 pixels at the edge, and then you need to also free the blocker afterwards. So that's already another 3 skills: one to block, one to dig away the steel, and one to free the blocker.
4) Finally, even when you get past the framethrower into the bottom of the pit where the exit is, I think you need at least 2 more skills to create a path to the exit. You can't just build up to it because the framethrower reaches a small portion of the left end of the terrain where the exit sits.
Even if there's some way in #3 to clear pixels and free the blocker with the same skill, you still end up with 7 total.