Vile Deathroach
Source: Pet Battle. Every deathroach is technically considered vile, but these really take the cake. Critter type. Shares a spawn with Deathroach and Scurrying Mawrat within the Beastwarrens. Follow the roads for the spawns.
The Vile Deathroach is a wild pet found in the Beastwarrens zone of the Maw during Shadowlands, obtained by defeating Deathroach and Scurrying Mawrat in pet battles until one spawns.
Guide awaiting review
Head to the Beastwarrens
Travel to the Beastwarrens in the Maw and follow the roads to find Deathroach and Scurrying Mawrat spawns. A confirmed spawn location is at 45.81, 65.74 in the Maw.
Defeat pets in battle
Engage Deathroach and Scurrying Mawrat in pet battles — defeating them in battle is the only way to despawn them and trigger a chance for a Vile Deathroach to appear. You cannot kill them physically to force the spawn.
Try after weekly reset
Log in shortly after the weekly reset and run laps along the roads of the Beastwarrens, battling every Deathroach and Scurrying Mawrat you encounter. Equip 
Comfortable Rider's Barding on your mount to avoid being dazed while running between spawns — Druids should use a mount rather than travel form for the same benefit.
Tips
The Vile Deathroach is a rare spawn, so it will not appear every time you clear the other pets — players have reported seeing it spawn roughly 5 times across 40 battles.
When a Vile Deathroach does appear, confirm it is a battle pet and not simply a critter with the same name before engaging, as critter versions cannot be captured.
