What the achievement asks
Complete the Adamant Vaults, on any layer. Ten points.
The hard part is finding them. People search the portal room for a seventh wing, decide it must be a rotating weekly thing, and give up. It is not a wing at all.
Where the Adamant Vaults are
They are an extension bolted onto the end of a good run in one of the six ordinary wings. Two extra floors, reached through the floor 5 exit portal.
Two conditions open them.
The perk. Spend 100 Tower Knowledge on The Adamant Vaults in the Box of Many Things, in the main room before you take a portal. In a group only one person needs it.
The run. Clear layer 9 or higher in any of the six wings with a Flawless score, meaning 200 points or more. Twisting Corridors and The Jailer's Gauntlet do not count.
When it works, the game tells you in chat and the normal exit portal on floor 5 turns red. Walk into it.
Buy the perk before you start your Flawless runs, not after. Every layer 16 run for Flawless Master already clears the bar, so with the perk in hand this achievement costs nothing extra. Without it, you go back and do a seventh run for no reason.
Once you are inside
The score stops mattering. Skip the trash, take whatever powers you like, run to the end boss and kill it. That is the achievement.
Worth a look while you are there
The broker up there sells transmog at 1000 phantasma rather than the usual 300, which is a bleak thing to discover on arrival with 400 in your pocket. If you care about the appearances, hoard on the way up.