Farseer's Raging Tempest

Quest line for the class mount Farseer's Raging Tempest starts at [npc=117888] on Broken Shore after completing Breaching the Tomb with a Shaman.

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2. Carried On the Wind - go to your order hall
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4. Gathering of the Storms - talk to [npc=106521] to start the scenario
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6. Defeat [npc=120130] (interrupt his [spell=239455]), [npc=120129] and [npc=120128]
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8. Step on one of the little whirls to start the dialogue.
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[spell=241852] will be added to your mount collection automatically after turning in the quest.
Its color depends on your specialization:
Elemental: fire/red, Enhancement: air/white, Restoration: water/blue

On the elemental fire version of the mount, it emits a light and will light up dark areas around you. Like in caves, etc...

Awesome detail that Blizzard added!

I managed to piece together how to do this in War Within.

It was very, very frustrating to try to piece together all of this, I'm surprised no one else recorded this before.

I made an account specifically to fill in the blanks on this, so others don't have to suffer my pain.

You will need to complete the achievement Breaching the Tomb, but only once per account. If you've already played through the Legion story you won't need to do it again.

You also need to recruit all the followers from your class hall; in general, if there is an exclamation point in your class hall, complete the quest and you'll be good.

Here is how I did it with a Level 35 Shaman toon:

1. Start the Legion quests. I did this by going to the Hero's Call Board in Stormwind; my Shaman happened to be low enough level to pick up the starter. You're looking for this quest Legion: The Legion Returns. There are probably other ways to do this, but I haven't figured out how yet.

2. If you've done the scenario before, when you go to talk to Recruiter Lee in Stormwind harbor, pass in the quest and before the next quest pickup there will be a conversation option to skip the opening scenario. Otherwise, play through the scenario and get to Dalaran being teleported to the Broken Isles. Get your Dalaran Hearthstone.

3. Find the NPC in front of the well in northern Dalaran that gives you the quest to start the Shaman Class Hall quests.
You're going to need to do literally all the Class Hall quests.

Class Hall Quests Notes

REQUIRED ITEMS:
[item=124124] X 3
These drop off of bosses in Legion dungeons; I believe the last boss is guaranteed to drop one. You'll have to visit Eye of Azshara before you need them, so you can just farm out Eye of Azshara repeatedly until you get the 3 you need. These are needed for one of the quests you'll pick up in Deepholm.

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• As far as I know, you must complete every single quest available in the Class Hall to be able to get the mount. It is what I did.
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• You're going to have to do table missions as part of the Class Hall campaign, so parts of the Class Hall campaign are time gated. Meaning you may not necessarily be able to spam the whole thing out in a night. In general most of the missions take an hour, but some are two hours. There are something like 10 total.
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• You can overlap required missions. AKA, some of the quests require you to do 3 missions and 5 missions for the quest. When you send out your follower to do 1 of 3, 2 of 3 shows up in the log, etc.
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• You're going to need to recruit all the helpers you can for your missions; one type gives 15% and the other gives 30% success chance to the mission. They cost class hall resources but you'll get more than enough from just simply doing the class hall quests.
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• At some point, you'll get a quest to do 10 world quests. Legion World Quests can be unlocked by going to Khadgar in the Violet Citadel in Dalaran, and picking up and completing Uniting the Isles.
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• You're going to need to be able to finish [zone=7546], and [zone=8040]. I did both on normal and got what I needed. So you may need to level to around level 50 to solo it if you're underleveled.
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4. When you finally get to the part where hold up your Artifact in front of the Altar to unlock the alternate appearances, you should see the quest Champions of Legionfall show up at Deliverance point in the Broken Shore. You need this quest, but it may be phased for you.

If the quest is phased for you, you need to unlock the Broken Shore World quests by completing Armies of Legionfall, which should be available from Khadgar near the flight master in Dalaran. If you've done the scenario before you can skip it. Then you should be able to pick up Champions of Legionfall.

5. After completing the Champions of Legionfall questline (which will send you back to your class hall to recruit your final follower), you will finally seen the quest Carried On the Wind at Deliverance point. Completing the scenario will FINALLY award you the mount.

If anyone has information to fill in feel free to let me know and I'll update.