WoWDB

This summons Kosumoth the Hungering!

Go to Drak'thul at 37, 71 on Broken Shore Map and talk to him. Then go to cave at 57,52 on the broken shore and click the mud at the end of the cave to get the  Weathered Relic you need. Then go to Drak'thul at 37, 71 on Broken Shore Map again and give him the relict and talk to him several times until he wants to leave him alone. After that click all the orbs in the right order!

Clickable order:
1. 38, 37 Cave Aszuna
2. 32,75 Stormheim
3. 41, 80 Val'sharah
4. 32, 72 on Broken Shore Map
5. 59, 13 Cave Aszuna
6. 67, 14 on World Map, under the neutral shark is the cave entrance
7. 56, 38 Highmountain
8. 53, 26 Cave Aszuna
9. 49, 90 on World Map in the sunken ship
10. 37, 71 on Broken Shore Map

This will summon the Boss and give you a Worldquest to obtain the  Fathom Dweller mount or the  Hungering Claw pet! I think it changes weekly.
After clicking the last orb a region wide message appears:

Thanks to all people who helped figuring this out.

Every two weeks, actually, according to @muffinus.  Also, RNG means that you could see the pet again (for NA region) or even just receive gold.

Anyone know if we have to collect the orbs each week, or once we do them, we're good forever?