Here is a breakdown of all steps with short instructions and timing. As of 5.4 this should take anywhere between 8 and 15 weeks to complete.
Chapter I: Trial of the Black Prince (1-2 Weeks)
The timing assumes you wait until you're on The Strength of Ones Foes quest before entering any raids, and do every raid available.
Alliance:Speak to Brewmaster Tsu or Seer Yong to recieve [item=87262], which starts [quest=31488]. Go see Wrathion in the Tavern in the Mists.
Horde:Speak to Kurong Caskhead or Cook Tsu to recieve [item=87262], which starts [quest=31488]. Go see Wrathion in the Tavern in the Mists.
[quest=31454] - share a drink with Wrathion and listen to his story.
Trial of the Black Prince - obtain Honoured reputation with [faction=1359], requires a couple of hours of grinding, depending on your spec and gear it can be faster. Most level 90 humanoid mobs and rares provide reputation with [faction=1359]. Best place to grind rep is probably Isle of Thunder.
The Strength of One's Foes - collect 10x[item=87208] and 10x[item=87209]. They drop in all Pandaria raids on any difficulty. This includes: Mogu'Shan Vaults, Heart of Fear, Terrace of Endless Spring, Throne of Thunder and Siege of Orgrimmar. Should be able to obtain within 1-2 weeks, depending on you luck. Leave Terrace for last, in case you get enough drops in other raids, so that you can complete the next step without having to do it twice.
Fear Itself - get a drop from Sha of Fear, the final boss in Terrace of Endless Spring. If you already cleared Terrace during the lockout, you can still come back on LFR and kill Sha of Fear again to get the drop.
Breath of the Black Prince - speak to Wrathion and get your first (now pretty useless) reward - a legendary weapon gem with +500 to your primary stat. Can only be used in Sha-Touched weapons from Heart of Fear and Terrace of the Endless Spring raids.
Chapter II: Wrathion's War (3 Weeks)
The timing assumes you do not obtain any Valor Points in the first week until you're on [quest=32474] quest.
Alliance:Meet the Scout/Horde:Meet the Scout - fly over to Krasarang Wilds to talk to an NPC
Alliance:A King Among Men/Horde:The Might of the Warchief - complete a simple kill quest in Krasarang Wilds
Alliance:Lion's Landing/Horde:Domination Point - unlocks a quest hub in Krasarang Wilds
Incoming... - speak to Wrathion
[quest=32474] - get 3,000 valor points. Any valor gained prior to picking up this quest does not count. Takes 3 weeks if you haven't got any valor yet the week you get this quest.
The Measure of a Leader - speak to Wrathion
The Prince's Pursuit - obtain Revered reputation with [faction=1359], requires a couple of hours of grinding, depending on your spec and gear it can be faster. Most level 90 humanoid mobs and rares provide reputation with [faction=1359]. Best place to grind rep is probably Isle of Thunder.
Alliance:The Lion Roars/Horde:Glory to the Horde - win one PVP match in both Temple of Kotmogu and the Silvershard Mines.
Alliance:A Change of Command/Horde:A Change of Command - kill an NPC in Krasarang Wilds, can be done with a group of 2-3 players.
Alliance:Call of the Packmaster/Horde:The Soul of the Horde - speak to Wrathion and get your second reward - an extra socket for any weapon. Still pretty useful, but nothing ground-breaking.
Chapter III: Two Princes (6-12 weeks)
Timing assumes a weekly clear of Throne of Thunder and Siege of Orgrimmar bosses that drop relevant quest items.
The Thunder King - speak to Wrathion
Meet Me Upstairs - speak to Wrathion again
Secrets of the First Empire - collect 20x[item=94593] and 40xTrillium Bar. [item=94593] drop off any boss in Throne of Thunder, as well as the first 8 bosses of Siege of Orgrimmar. The raids can be done on any difficulty. My experience on 3 characters, as well as talking to guildies leads me to believe you can expect anywhere between 2-6 [item=94593] per week, assuming a full clear.
I Need a Champion - obtain Exalted reputation with [faction=1359], requires a few of hours of grinding, depending on your spec and gear it can be faster. Most level 90 humanoid mobs and rares provide reputation with [faction=1359]. Best place to grind rep is probably Isle of Thunder.
The Thunder Forge - complete a single player scenario
Spirit of the Storm Lord - use a quest item on Nalak, a world boss on the Isle of Thunder, and stay alive for 10-15 seconds while it channels and charges up. Best done in a raid group.
The Crown of Heaven - speak to Wrathion and collect your third reward, a very powerful legendary gem that goes in the meta slot of your head item. You can get extra ones for the price of 5xPrimal Diamond.
Echoes of the Titans - collect 12x[item=94594]. These drop off the last 6 bosses of Throne of Thunder and the first 8 bosses of Siege of Ogrimmar. My experience on 3 characters, as well as talking to guildies leads me to believe you can expect anywhere between 1-3 [item=94594] per week, assuming you kill all bosses. Lei Shen is guaranteed to drop a [item=94594] every week.
Heart of the Thunder King - get a drop from Lei Shen, the final boss in Throne of Thunder. If you already cleared Throne of Thunder during the lockout, you can still come back on LFR and kill Lei Shen again to get the drop.
Chapter IV: Celestial Blessings (less than 1 hour)
A Reckoning - speak to Wrathion
Celestial Blessings - fly around Pandaria and visit the various temples and speak with Celestials. This will take you to Kun'Lai Summit, Townlong Steppes, Jade Forest and Krasarang Wilds. In addition to speaking to the Celestials, you will have to fight Wrathion at one of the temples and complete a role-specific challenge.
Cloak of Virtue - Speak to Wrathion to get your next reward, an epic item level 600 cloak. Do not waste your valor upgrading this cloak, as you will be getting your legendary soon which already comes upgraded to item level 608.
Chapter IV: Celestial Blessings (1-2 hours)
Timing here assumes getting as far as the cloak, does not include the Garrosh Hellscream kill.
Preparing to Strike - Speak to Wrathion
Meet Me Back at the Inn - Speak to Wrathion
A Timeless Discovery - Speak to Wrathion
Secrets of the Timeless Isle - Collect 5,000 timeless coins. You get coins for almost anything you do on the Timless Isle - killing mobs, looting chests, completing quests and even skinning, herbing and mining. You get a lot of coins from doing the introductory quests on the Isle, and I recommend looking for chests and rares for quick coins.
The Emperor's Way - You have to defeat the four Celestials on the Timless Isle. They are all always available to be killed, but only one can be engaged in combat at a time. This is best completed with a full raid.
A Pandaren Legend - Speak to Wrathion and get your legendary cloak. The cloak comes upgraded to item level 608.
Judgment of the Black Prince - Kill Garrosh Hellscream, the last boss in Seige of Orgrimmar.
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