Edit:
This is the description of what we have to do, from Wowhead:
To unlock the toy N'lyeth, Sliver of N'Zoth, you will first need to turn War Mode on and become an Alliance Assassin or Horde Assassin by killing 10 players of the opposite faction without dying in Kul Tiras or Zandalar. The moment you reach Assassin, you will be offered a new quest from an unseen presence (presumably N'Zoth himself), requesting you to prove your worth to him by slaying members of your own faction.
There are two versions of this quest: Servant of N'Zoth for Alliance players, and Servant of N'Zoth for Horde players.
By accepting the quest, you will receive N'lyeth, Sliver of N'Zoth, which can be used to transform your character into a Servant of N'Zoth, but be careful - Using the item will damage you by 60% of your maximum health, so make sure you're fully healed before using it! The effect is quite cool, covering your character in tentacles and a void aura. The effect lasts for 1 hour.
The quest requires you to kill 10 of your own faction's members without dying. Dying at any point will automatically fail the quest, and you will need to reach Assassin again to start the quest over.
Completing the quest awards you a toy version of N'lyeth, Sliver of N'Zoth that allows you to become a Shath'yar without requiring reaching Assassin, as well as the Feat of Strength Servant of N'Zoth, which awards the title %s, Servant of N'Zoth. According to N'lyeth, Sliver of N'Zoth description, you are able to become a Servant of N'Zoth in Kul Tiras, Zandalar, Uldum and Vale of Eternal Blossoms.