Blind Rat
From Marcus "Bagman" Brown. Do you see how they run? Critter type. Since comments are not making very clear how annoying it is to go after this pet, here is my personal experience: 1.
Blind Rat is a wild battle pet found in the Dalaran Sewers (Underbelly) during the Legion expansion, where it can be caught through pet battles in that dangerous PvP-enabled zone.
Guide awaiting review
Reach the Underbelly
Head into the Dalaran Sewers (Underbelly) and locate Raethan, the Underbelly Guard Captain, at the eastern entrance at 68, 58. Pay him 
5 gold for a Hired Guard, who will protect you from other players for 5 minutes — roughly matching the cycle between Sewer Guards being present and absent.
Manage your Hired Guard
The Hired Guard lasts 5 minutes, so avoid sprinting or using movement abilities that outpace them, as they will despawn if left behind. Consider putting the guard on focus and marking them with a raid icon so you notice quickly if they expire.
Camp and catch Blind Rat
Blind Rat can be killed by other players' AoE before you reach it, so the most reliable approach is using a stealthy character to wait hidden until one spawns, then engaging when the area is clear or when Sewer Guards are present. If you get tagged by another player mid-battle, the pet battle will end and you must exit combat before trying again.
Tips
Each Blind Rat battle rewards 75 Sightless Eyes, so expect competition from other players also farming the zone.
Blind Rat's name, description ('Do you see how they run?'), and its ability Lullaby are all references to the nursery rhyme 'Three Blind Mice.'
