Not 100%, but i dont think so. I did all the operation kills on a different toon (Unless it counted kils pre-2.0) then the one i killed the mobs with.
None of the kills are retroactive not even the world boss even though i had the achievement for killing it pre 2.0 i had to do so again for Datamining
As far as i know it doenst require all to be on the same characther..nothing in the achievement system requires this
I think..maybe the exploration ones
But i cant say for sure cause personally i did it all on my sin