Hiya, so I got the achievement for 300 arena wins which rewarded in a cool tabard, even though I got the achieve on all my characters, only my char who earned it got the tabard. Do I have to complete it again on another char for the tabard?
Nah, I disagree with your elitist mentality.
Tier gear should be available during the leveling process. I don't want to have to mingle with these eltitist jerks in LFR to get gear as it is. I pay a sub fee, I shouldn't have to do LFR to get raid gear, much less Flex or Normal.
Brutally dedicated isn't an account-wide achievement. It will still show up on other characters, but if you hover over it, it will tell you which character got it. That probably means you can't get the tabard on other characters, unless you re-do the achievement on those.
It's different from an achievement like The Loremaster. When you get that, all your characters get a tabard in the mail upon logging in for the first time after earning it.