Call me strange, but I think "Achievements" in DF are a terrible idea.
DF is an extremely player-driven game. The things players achieve are highly emergent and rely on player innovation. We don't need some kind of hand-holding system to congratulate you for building a tall tower or a staircase or something, and really, I don't see what good that would do anyway. I mean, congratulations, you built a fortress with a given total wealth, or a huge magma pit, or a stairway to heaven; DF players, by and large, aren't the sort of people who need some kind of artificial reminder that they did something awesome, and even if they were, the great things people do in DF are the weird things that people have not (or simply have rarely) done before.
To put it more concisely, this isn't X-Box Live and I don't think your average hardcore DF player is going to need the machine patting him on the back for something like this, and I think that giving players a checklist of accomplishments will, if anything, stifle creativity by giving players too much of a stock list of Canonically Awesome Things to do, while completely ignoring actual innovation. It would just encourage people to do a bunch of stuff on a list as opposed to engaging in good old-fashioned dwarven ingenuity (e.g. ice cube fall traps, automated fortress systems). I just think it would promote the wrong kind of mindset about the game.
Also, even if it were a good idea, implementation would be a bitch. The game would need to be constantly checking to see if you're doing things which fit a certain pattern (such as a bunch of staircases N levels high), and I have no clue if that would be feasible whatsoever for a lot of the ideas mentioned, and even if it were, it would probably be somewhat involved and not be worth the time. After all, why would Toady want to spend that much time coding something which doesn't actually do anything except tell you that you've done what you already know you've done?