What the achievement asks
Reach Exalted with the Rajani. Five points, account-wide, both factions.
The Rajani are the Vale of Eternal Blossoms' patch 8.3 faction, and their reputation comes from the zone's assaults and daily quests.
Paced by the rotation
One assault runs in the Vale at a time, and reputation comes with its objectives and dailies. Exalted is therefore a matter of weeks of turning up rather than a grind that can be concentrated into a weekend.
Take every assault, not only the Black Empire one. All three award Rajani reputation, and waiting for a particular assault roughly doubles the time to Exalted.
Its counterpart
Uldum has its own faction, Uldum Accord, earned the same way in that zone. Both are needed.
Because the assaults alternate between the two zones, neither reputation can be pushed on its own: whichever zone is active is the one paying out today. The practical approach is to do whatever is running and let both climb together.
Anyone finishing Defend the Vale is doing this work already.