ok so skill drain has always been a tricky card but here is what i know about it. It negates the effects of face-up monsters while they are on the field. It does not stop these effects from activating and if the monster leaves the field before it resolves then skill drain can no longer stop its resolution.
Therefore the trick to this puzzle is most likely to use the Enemy Controllers/Book of Moon to tribute/flip face down a monster after activating its effect so it is no longer face-up on the field when it resolves and is therefore not negated by skill drain.
That should be enough to start somebody off. Surely we can figure out from there how to either take out swords and attack to win or maybe even burn him somehow with cowboy or something. I cant work out a scenario right now, but im sure i will eventually.