In what little testing I did, I believe achievements are per character, not account. That said, I don't know of any which can't theoretically be gotten (although some have ridiculous requirements, like the 10k leves)

On an unrelated note, I do have to say far too many of the achievements come off as lazy or uninspired. Way too many "Do [Activity] # of times" as opposed to even slightly creative achievements like "Find Hard-to-reach Locale" or "Kill [Boss] in [Unique Condition]".