What the achievement asks
Unlock 150 doors inside the Zskera Vaults using Zskera Vault Keys. Fifteen points, account-wide.
What a Zskera Vault is
A vault is a tall circular chamber of four floors, each with seven or eight sealed rooms. One key opens one door. The layout stays the same every week and only the contents behind the doors rotate, so after your first run you already know the building.
A full vault is 28 or 29 doors, which makes 150 doors six complete vaults.
You do not have to loot everything or work out the puzzles behind the doors. The achievement counts doors unlocked, nothing else. Solving a room only matters if you are trying to climb higher in the vault or if you are still missing books for Librarian of the Reach and While We Were Sleeping, several of which only appear inside.
The real gate is the week, not the keys
A character can only work through one vault per week. Six vaults therefore means six weekly resets on a single character, and no amount of key farming shortens that.
What does shorten it is alts. Progress has been account-wide since patch 11.0, so six characters in the same week finish this from zero. If you have a stable of level 70s, this stops being a month-and-a-half achievement and becomes a weekend.
Getting 150 keys
Buy them. Since patch 10.1.5 the renown envoys at Dragonscale Basecamp sell keys for 50 Dragon Isles Supplies each. A hundred and fifty keys is 7,500 supplies, which sounds enormous until you remember supplies pile up from every Dragon Isles activity and most returning players have thousands sitting unused.
Farm them. Keys drop from the rares of the Forbidden Reach, almost reliably, and from its treasures. If you are already working through Hoarder of the Forbidden Reach, which wants a hundred treasures, the keys arrive as a side effect and you may never need to buy one.
Mail them. Keys are account-bound. Every alt can farm or buy on its own and post the keys to whoever is doing the vault, which is what makes the six-character route practical.
Where it fits
One of eleven under You Know How to Reach Me, a piece of A World Awoken. One of your six runs also gives you Every Door, Everywhere, All At Once for nothing, provided you go in with enough keys to clear that vault in a single week.