Okay, here's how it's done:
1) First lemming mines as shown in picture #1. Position must be pixel precise, so that a positioning glitch causes him to fall all the way down but the others to land on the middle platform as shown in picture #2.
2) Make the first lemming a floater.
3) Second lemming (first lemming on middle platform) digs about half way up the slope, third lemming blocks right behind him, as shown in picture #3 (if the third lemming doesn't block, he'll go over the top and drown. He'll be freed after the digger takes a few digs, but the delay is enough to stop him from being able to go up).
4) The floater builds over the trap, as shown (as if it was nessecary to show that, though...) in picture #4.
5) 100% saved, and with 9 seconds to spare, without using the basher, as shown in picture #5.
My question now is: Can you, by placing them with perfect timing, make a basher free a blocker but still turn around on him (by placing the blocker in the mid-bash higher area, the part that you put new bashers in for the trick used to beat Fun 12/14 with bashers only)? If so, then it's possible without the digger (but using the basher instead), thus making the miner and the builder the only compulsory skills for this level (and that's assuming we don't find solutions without them). No way I'm going to try this myself, at least not until I get confirmation that it's at least possible in general.