What the achievement asks
Upgrade Ashjra'kamas, Shroud of Resolve to rank 15. Ten points.
This one is not tied to your account. The cloak belongs to the character that earns it, and so does the achievement.
What rank 15 actually costs
The cloak is upgraded by running Horrific Visions, and each rank asks for more than the last. The floor is around twenty-two runs, which needs roughly 200,000 Coalescing Visions beyond the two free Vessels the patch 8.3 questline hands you.
Coalescing Visions accumulate from the daily work in Uldum and the Vale, which is why the pace is set by how often you show up rather than by how well you play.
What each rank wants
The requirement changes shape as you climb, and knowing when it changes saves wasted runs.
- Ranks 2 to 5 need the vision's boss killed.
- Ranks 6 to 11 stop asking for the boss and start asking for side areas cleared, one, then two, then all of them.
- Ranks 12 to 15 want the lost areas, the deepest parts of the vision.
From rank 11 onwards, a single run per rank is enough provided you clear both lost areas within your sanity. If you cannot hold out that long, the same rank takes several runs instead. That is the real difference between a month and two.
Doing it alongside everything else
Every run also earns Corrupted Mementos, which We Have the Technology needs 69,600 of, and the research those mementos buy is what makes the hardest visions survivable.
The two feed each other: better research means deeper runs, deeper runs mean faster cloak ranks, and a rank 15 cloak is what makes The Most Horrific Vision of Stormwind and of Orgrimmar realistic.