As with everything else concerning fishing in WoW, El'x Extreme Anglin' is your best buddy and a fantastic source of information on where to find fish, drop rates, information on pool spawns, and Fishing achievements.
Accomplished Angler is a very work- and time-intensive meta-achievement, so I've taken the liberty of splitting this guide up. The first set of achievements you'll need:
Grand Master Fisherman
Sorry, folks, there's no real way to shorten this one; you've just got to keep fishing. One of the nice things about the profession is that you can level it anywhere -- the only penalty to leveling it in an area with higher "fishing skill" than you currently have is the amount of junk you'll catch versus actual fish. But on your way to Grand Master, you'll have put a lot of work in towards: