Already have diety done. I did it because I thought it would give me all the difficulty achievements at the same time.
But like I mentioned, nope. The devs decided you need to do every single difficulty level.
There's two types of achievements in regard to difficulty. There is the basic one, which comes down to beating the game once on every difficulty, and the description reads 'beat on X difficulty'. I think you're referring to this one, for which indeed beating a higher difficulty doesn't clear the lower ones.
Then there's the one I was referring to, which is mostly related to scenarios, and the achievement description reads as 'beat on X difficulty or higher'. For these achievements beating the game on diety clears all others. So for example beating the Mongol scenario on diety will get you at least 3 difficulty related achievements (diety, inmortal and emperor, maybe also king, I don't remember if there is one for king).
Anyway, if you're about hunting the first mentioned 'basic' difficulty achievements, you can do the Settler through King achiements in less than a hour, each time start on a duel sized pangaea map with only Venice as adversary, pick the Huns or another early powerhouse and simply walk through them. It's boring, but compared to some of the other achievements, especially scenario related ones, it's ridiculously easy and fast.