A second tab with all combined that if linked shows also the character.
[other_char_name: Occu'Thar] "This person has pwned Occu'Thar but on another Char"
1. There won't be a confusion if you got an achievement on a raid but you are now low ilevel so you shouldn't join (if that's what the leader wants).
2. People are happy that they can get a dreaded achievement on one char, but not have to log in "the old main" to do it.
3. This should be completely hidden unless a players opts to link an achiev from the "account-wide" tab. This is because it is obvious several people keep "hidden" chars.
edit: Since it has to be hidden, it is not extremely important for "prestige", mainly for linking.
However, one may opt to show that info publicly.
Unless everything is meshed with no information on char, but that may be too messy.