This quest line has just 5 missions to complete. Each one has a recommended light level that goes up by 10 with every mission. The King of Mountain is the first mission in this quest and has a recommended light level of 280 so you will need to be at least a light level 240 to even start it but I suggest being higher than that to make things easier for you. The other missions are as follows, in order they need to be completed:
The Walls Come Down
The Iron Tomb
In between missions you will be visiting the Iron Temple to talk to various quest givers and such so they can update you on where you need to go next. Once you finish The Iron Tomb mission, head back to the temple and speak to Shiro-4 and then to Tyra Karn and the achievement will unlock once you have talked to her.