To do this quest, you have to do the event when it appears in the Warrens.
Similar to the [spell=347208], you'll see a big event icon appear in the Warrens when it's live. The specific event changes every week--the one I did doesn't even seem to be in the database yet (Hunt: Anima Devourers). It works the same way as the [spell=347208]. Progress the bar by killing the relevant mobs mentioned for it until the bar reaches 100%. The bar is progressable by anyone in the area, not just your own kills. A boss will spawn when the bar is 100%, and you kill that.
Be warned that the mobs needed for the one I did were all elites that hit pretty hard, and the boss was also pretty beefy. I do not recommend attempting to solo them as a non-tank, and it might take a tank a good while to kill anything solo. There wasn't anyone there at all when I did this with a friend, and I'm on a very high pop server. Bring friends or a premade!
Also, since I see a lot of comments about needing war mode on, we were war mode off when we did this.
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*Note: If this was bugging out for anyone previously, they applied fixes.
Patch notes for December 10, 2020: https://worldofwarcraft.com/en-us/news/23580183/hotfixes-december-11-2020
Fixed an issue that prevented completion of “Stalking the Warrens” after successfully completing a Hunt in the Maw.
Patch notes for December 14, 2020: https://worldofwarcraft.com/en-us/news/23580183/hotfixes-december-14-2020
Resolved an issue where Hunts could sometimes not progress to the next stage.
Patch notes for December 17, 2020: https://worldofwarcraft.com/en-us/news/23580183/hotfixes-december-22-2020
Fixed an issue where Hunting Party credit was not earned after the Hunt scenario was completed.
Patch notes for December 18, 2020: https://worldofwarcraft.com/en-us/news/23580183/hotfixes-december-22-2020
Fixed an issue that could prevent the respawn of feeding rituals during the Shadehounds Hunt to not respawn.
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*Edit: If it's still bugging out for you, you can report this in-game via Esc > Support > Submit feedback or bug report.