This is a side quest from the DLC. There are two ways to trigger it:
Find a book called "The Aetherium Wars."
Go to Arkngthamz and meet Katria's ghost.
This is a somewhat lengthy quest, and you will need a good number of lockpicks and a decent lockpicking skill (I was around 60). Also, bring a crossbow/bow and a good supply of arrows/bolts. Projectile-style Destruction magic also works for the tonal locks.
The book "The Aetherium Wars" can be found in these locations:
Dawnguard Fort
Castle Volkihar Undercroft
Bard's College
Hall of the Vigilant
Ruunvald Temple
Objectives:
Reach the summit of Arkngthamz.
Solve the tonal lock.
Claim the treasure of Arkngthamz.
Speak with Katria.
Search for Aetherium Shards.
Locate the Aetherium Forge.
Retrieve the Aetherium Crest.
Stand clear.
Find the Aetherium Forge.
Shut off the steam.
Defeat the guardians of the forge.
Speak with Katria.
Use the Aetherium Forge.
The tonal lock requires a crossbow to complete. You must shoot each of the 5 parts in a certain order to unlock the door: bottom left, bottom right, top left, top right, middle.
You also have the option of getting more materials to use at the forge. If you only want the achievement, skip this extra part of the quest. Use the forge to make one of the three items, and the achievement will unlock when you finish using the forge.