I think achievements should be world based, this way some one can start a new world and get them all over again. and as far as achievement storing it should store how many times you got it. I thought of this manly because of the Xbox, I just love getting them and a way to get them over again would be nice.
copy and pasted from Suggestion area. link to old post http://www.minecraftforum.net/viewtopic.php?f=1&t=303119