Sorry to say this, but at first glance this doesn't seem very interesting -- I could be wrong, so I don't mind leaving this open for a while to see what emerges.
We already have
Skills you can't live without, so any level that can be solved without builders is a guaranteed "yes" for this challenge. For levels where you do need builders, I would guess it's mostly a matter of the save requirement: on Fun/Tricky levels where you can afford to lose lemmings, you can bomb away the bridge after using it. On others, you can't.
That means:
Fun: All levels should be solvable, even Level 7, since you can use the nuke to destroy the bridges.
Tricky: 19 is not possible. 23 is possible (use the reverse miner solution, and destroy the bridge with a basher). 24 is possible with bombers. 25 is most likely possible with a landing platform solution and the nuke. 27 and 28 should be possible with bombers.
Taxing/Mayhem will have a lot of impossible levels, but it seems fairly straightforward to look through the list and decide which ones are possible and which aren't.