So, the way I would be doing most achievements is:
Require the player to actually do something and not just progress through the game.
Try to make the objectives more obscure/weird/unexpected/challenge based and mostly have nothing to do with the main story of the game.
So what I'm saying is that achievements would be a "side-thing" so to say.
But yes, I agree with pretty much everything you said.
In any case, looks like achievements are probably going to stay based on feedback. :)