After a helpful guildie mentioned that The Crumbling Hall was up as one of the Golden Lotus dailies, I immediately started going about getting that half of the achievement done.
Initially I'd thought the quest would be easy, since everything I'd read about the Achievement said that The Thunder Below was harder. However, I tried going slow, going fast, using Camouflage as much as possible, shuffling my pet ahead of me, starting the quest with a random person sharing it with me at the first wall so that I wouldn't have to go through the front part of Guo-Lai... and found after numerous restarts that it really *isn't* easy at all.
Also, unlike Roll Club, which I also had an incredible amount of difficulty completing (although to be fair, it was mainly due to motion sickness and Aussie latency rather than any lack of skill I happen to have), I only had that day to do the quest before it reset... meaning that if I missed it, I'd have to wait until the next time the quest was up.
As luck would have it, I finally managed to follow someone on the same quest through the halls, letting them activate statues ahead of me and hearthing out to hand the quest in at the end with only 20min to spare before daily reset.
I suppose after all that, it was actually a really good challenge... which makes a change from doing the same dailies over and over. I really should look at the achievements list more!