You get this achievement for defeating the commanders of each flying fortress. The fortresses can be cleared in any order.
The entrances to three are in Orobas Fjords: Stone is at the east end of the island in the channel. Raze is across from Champion Harbor, and Kaera is south of Champion Harbor and east of Red Hammer Shrine.
The fourth tower is Kali: past the south exit of Orobas Fjords.
The last two towers are in the Broken Valley. Geshniz is in the far northwest and Rayhum is in the far northeast (where the village used to be).
The strategy for each tower is the same: Fly around as a dragon killing all of the towers that shoot things at you. Then land in the headquarters and enter the teleporter.
Once inside, navigate the (usually very short) interior and kill the boss. Most bosses can be mindread for better loot and most are involved in one of the quests used to upgrade your Battle Tower.