Discover the secrets of the mogu with Wrathion, and deliver to him the heart of the Thunder King.
This achievement is earned by completing the third portion of the Mists of Pandaria Legendary quest chain.
Mists of Pandaria Legendary Questline
Quests in Chapter III
How to Complete Chapter III
To start, head over to Wrathion at the inn at The Veiled Stair and "meet him upstairs". Wrathion will give you the quests Secrets of the First Empire and I Need a Champion. For I Need A Champion, simply grind to Exalted with The Black Prince reputation using mobs on the Isle of Thunder.
Secrets of the First Empire takes far longer and is one of the two big hurdles for Chapter III. You must kill the bosses in Throne of Thunder to get the 20 Secrets of the Empire needed to complete the quest. Unlike the Sigils from Chapter I though, you only get one chance per boss per week, regardless of difficulty. All difficulties have the same drop rate as well. This means that if you kill Jin'rokh the Breaker in LFR difficulty, you will -never- receive a Secrets of the Empire from Normal difficulty Jin'rohk until the week is over. The drop rate is decent but it is lower than the Sigils from Chapter I and will probably take you at least 4 weeks to complete.
After collecting the Secrets, the Trillium Bars, and getting your reputation to Exalted, meet Wrathion back at his inn and turn in the quests. He will then give you the quest The Thunder Forge and ask you to meet him on the Isle of Thunder. You must travel to the Isle of Thunder and help Titan constructs fight off Sha while Wrathion works on the Thunder Forge. This can be tricky for certain for certain classes and specs because you must keep the Titan constructs alive or you will fail, and they have little health. The final boss of the event also hits very hard if you don't interrupt his casts with the anvil's stuns, so you can flat-out die to the damage he deals if you're not careful.
Wrathion will request one final thing from you before you get your Legendary meta gem - the spirit of Nalak. Go back to the Isle of Thunder and fight Nalak, the Storm Lord. While you can complete this quest solo, it is very tricky because Nalak will kill you very quickly. It is far easier to just stick to a raid group that is doing the fight and then casually throw your Lightning Lance at Nalak, complete the quest, and walk away. Meet with Wrathion and receive your reward in The Crown of Heaven.
Wrathion will now have you go back into Throne of Thunder for Titan Runestones. This time you need 12 of the item, but they drop much more rarely than the Secrets and they can only be found on the second half of the bosses - Durumu the Forgotten, Primordius, Dark Animus, Iron Qon, Twin Consorts (Suen and Lu'lin), Lei Shen, and Ra-den (heroic difficulty only). A hotfix changed it so that Lei Shen will now always drop a Titan Runestone, which makes 12 weeks the maximum amount of time you could spend on this quest.
Afterwards, you simply go to Wrathion, accept Heart of the Thunder King, and go kill Lei Shen (though you've probably been killing him all along anyway) and loot the Heart of the Thunder King from his corpse. Note that you may loot a Titan Runestone in the same week that you loot his heart - they are not mutually exclusive. Upon turning in that quest, you will receive this achievement for completing Chapter III.
Also, click on any of the quests for individual details - Aliok has nice walkthroughs in the comments of each quest.