DANGER: Kosumoth the Hungering

If you got the pet [item=140261] one week and then are wondering why you aren't getting the world quest the following week for the mount [item=138201] (or vice versa) - the world quest is on a 2 week cooldown - confirmed by @muffinus

.@zyrusha repeat time on that is every 2 weeks

Link

Also, because you got the pet one reset it does not mean that you will get the mount as a reward the next reset. You could get the pet again, or even gold.

How to get the World Quest for Kosumoth that will reward World Quests in Eye of Ashara resulting in the Fathom Dweller Mount and Hungering Claw Battle Pet.

This is my guide on how to get the Fathom Dweller Mount. This is a step by step guide. TomTom is needed for this guide so head over to curse.com and pick up that addon. After completing this you will now get World Quest for DANGER: Kosumoth the Hungering, it will award 2 things one week it awards a pet or mount then the other in two weeks.

TomTom from Curse: https://mods.curse.com/addons/wow/tomtom

Go to Drak'thul at 37, 71 in the Broken Shore Map and talk to him. Now head to cave at 57,52 in the broken shore and look for the mud pile at the end of the cave to get, click on it and receive the Weathered Relic, it adds an item to your bags. Head back to Drak'thul at 37, 71 on Broken Shore Map again and talk to him several times until he wants to leave him alone or go away. Now its time to go around the world and click orbs in the right order.

Below is a the TOMTOM coordinates for each orb, each one is in my video with specifics.

Drak'thul:

/way Broken Shore 37,71 - Talk to Drak'thul
/way Broken Shore 57,52 - Cave with Mud pile to loot Weathered Relic
/way Broken Shore 37,71 - Talk to Drak'thul Again

Orbs:

/way Azsuna 37.96 37.41
/way Stormheim 32.92 75.90
/way Val'sharah 41.51 81.18
/way Broken Shore 29.16 78.57
/way Azsuna 59.37 13.13
/way Broken Shore 67.26 14.90
/way Highmountain 55.84 38.47
/way Azsuna 54.02 26.18
/way Eye of Azshara 79.52 89.31
/way Broken Shore 37 71

Now you must log out or change zones for the World Quest to appear. This will summon the Boss aka Kosumoth the Hungering in open world Eye of Ashara and give you a World Quest to obtain the Fathom Dweller mount or the Hungering Claw pet! It changes either weekly or bi weekly.

Here is my video of the Quest Chain where I go into much more detail:
https://www.youtube.com/watch?v=E4vmOuAksFo

This is the video guide I used https://www.youtube.com/watch?v=0Gy4iJGhD_E I am simply adding some coords and minor details to make it a bit easier to get through, full credit to Argathen.

Drak'thul is on the Broken Shore island at 36, 71
The cave is at 56, 54 (approximately, forgot to check coordinates while I was there) (under the Horde gunship ruins) - the dirt pile is very easy to miss, so just mouseover in the back right corner of the cave 'til you find it
When you return to Drak'thul to question him about the Weathered Relic, he will only have one line of chatter each time, you must hassle him

First cave entrance is at 37, 37 Azsuna - the base of the tree, between the roots is a bush - jump through the bush and it's beneath that

Second cave is between Suramar and Stormheim (Stormheim map coords, I beleive), 32, 76. There is an elite named Kangaxx inside the cave, easy enough to walk around her patrol, orb is in the back left of the cave

Third cave - 41, 81 Val'sharah - behind the tree root and under a bush again. In the cave, you have to do a small U-turn and jump over a rock (look to the whisp) and there will be an elite with 1.66m hp, Arcane Servitor, his arcane missiles hit incredibly hard (500k-690k), so interupt them or cc him if possible. The orb is behind him on the left.

Fourth cave - 31, 77 Broken Isles (near Drak'thul). Under water, right on the fatigue line, make sure you clear fatigue before swimming down and/or have increased swim speed. The cave is below a big overhanging rock thing, just go under it. Orb is in the back under the little tent looking thingy, do not get hit by the steam geysers as they hurt a lot.

Fifth cave - 59, 12 Azsuna in the purple crystal crater thingy (right near where mage's can teleport to), cave is at the base of one of those big purple tree thingys.

Sixth cave - 67, 15 Stormheim not quite in the fatigue zone, near the ruins of a statue, swim down directly below "Toothless Great White", a neutral, never moving, targetable mob. In this cave are steam geysers again, do not get hit by them.

Seventh cave - Highmountain, take the flightpath to skyhorn, then go through the harpy nests in the haglands and there is a path that leads up the mountain at about 54, 34. Follow this all the way to the top, then looking out over the water you can jump down, or if you want to be sure, use a goblin glider kit to safely fly right to the cave entrance at 56, 37, half way down the mountain with no direct path to it. NOTE: there is a big obvious cave entrance, this is not the one you need, you need the one just to the right of it, behind a bush. The orb is inside the mouth of a dinosaur skeleton.

Eighth cave - 53, 26 Azsuna at the base of a tree, under the bushes. orb is in the back of the cave, just behind the pillar under some leaves.

LAST ORB: 79, 89 Eye of Azshara (not the instance, the island zone). Swim directly down and you'll see an upturned ship, the ship is a bit of a maze, would recomend using the youtube video guide linked at the top if you have trouble with it or don't have any water breathing buffs.

Once you have clicked all the orbs, head back to Drak'thul on the Broken Shore Island at 36, 71 and he has another orb on his table for you to click on, after that he will have a bit of dialogue then the world quest opens up for your character forever more.

PLEASE NOTE as afore mentioned, this is not my guide and I do not claim any credit for it, I have simply added some coordinates and small notes to the video linked at the top of my post.
Hope this helps.