Filthy Slime
Drops from Gol'than the Malodorous. You're not entirely sure where this came from, nor do you really want to know, but you are sure that it does eat a tremendous amount of garbage. Magic type. Getting the pet is easier than you may think! To begin with, you need 5 people (EDIT: As of 8.3.7 it's soloable) in order to summon the rare.
The Filthy Slime is a Battle for Azeroth pet dropped from Gol'than the Malodorous in Tol Dagor, summoned by clicking the 
Filthy Bucket found in The Brig.
Guide awaiting review
Enter Tol Dagor
Enter Tol Dagor on Mythic difficulty and defeat the first boss. You can avoid most of the trash by going left and around the enemies.
Find the Discarded Cell Key
Head to the Drain (ground floor/sewer area) and clear trash toward The Brig. On your way, look for a 
Discarded Cell Key, which spawns in multiple random locations and is easy to miss.
Unlock the Cell
Once you reach The Brig, go to the third cell on your right and use the Discarded Cell Key to open it.
Summon Gol'than the Malodorous
Inside the cell, click the Filthy Bucket located in a hole in the wall to summon Gol'than the Malodorous, then defeat him for a chance at the Filthy Slime pet.
Reset and Farm Again
The Filthy Slime is not a guaranteed drop. You can soft reset the dungeon by running out and waiting approximately 30 minutes, then re-enter without needing a weekly reset. A recommended method is to also kill Jes Howlis before resetting, so that after a soft reset you spawn in the Jes Howlis room with trash already cleared, saving time on repeat runs.
Tips
The Filthy Slime is cageable, meaning it can be purchased or sold on the Auction House if you prefer not to farm it directly.
After killing Gol'than the Malodorous, create a group and leave the dungeon to get ported outside within one minute, speeding up the reset process.
