Shadowlands Safari

If you can't find the pet, you should be able to get it most of them as a secondary pet during battles. I recommend using Anubisath Idol. He is very tanky and can kill 3 pets by himself easily. Took me about 3 hours to complete. Only pet that gave me trouble was Clutch. I had to keep killing the other nearby pets to force him to spawn.

Here are the zones and a few spawn locations in each zone.

Bastion
- Copperfur Kit (42,60)
- Fledgling Teroclaw (43,60)
- Fluttering Glimmerfly (42,47)
- Glimmerpool Hatchling (50,64 or 46,29 or 54,32)
- Rustfur Kit (56,88 or 51,63 or 44,45 or 55,36)
- Vibrant Glimmerfly (anywhere in the zone)
- Wader Chick (54,73 or 54,81 or 53,85)
- Wild Etherwyrm (48,43 or 57,58 or 55,34)

Maldraxxus
- Animated Cruor (30,33 or 35,21 or 57,36)
- Bleak Skitterer (38,33 or 63,33 or 54,60)
- Crawbat (58,38 or 55,60 or 45,51)
- Necroray Spawnling (45,31 or 67,51 or 75,48)
- Pulsating Maggot (58,50 or 45,51 or 36,37)
- Clutch (31,30)

Ardenweald
- Verdant Kit (43,55 or 38,53 or 40,59)
- Decay Grub (60,30 or 66,22 or 72,37)
- Gorm Rootstinger (25,49 or 30,50 or 69,56)
- Deepwood Leaper (52,56 or 50,68 or 38,52)
- Starmoth (51,36 or 56,34)
- Tranquil Wader (55,61 or 50,57)

Revendreth
- Dusky Dredwing Pup (60,69)
- Lost Soul (50,32 or 52,76)
- Mire Creeper (56,59)
- Rosetipped Spiderling (47,75 or 56,55 or 75,56)
- Withering Creeper (63,55 or 75,59 or 46,68)

Because I was typing this out anyway:

Bastion:
/way 42 60 Copperfur Kit
/way 43 60 Fledgling Teroclaw
/way 43.2 58.1 Fledgling Teroclaw
/way 42 47 Fluttering Glimmerfly
/way 50 64 Glimmerpool Hatchling
/way 46 29 Glimmerpool Hatchling
/way 54 32 Glimmerpool Hatchling
/way 56 88 Rustfur Kit
/way 51 63 Rustfur Kit
/way 44 45 Rustfur Kit
/way 55 36 Rustfur Kit
/way 54 73 Wader Chick
/way 54 81 Wader Chick
/way 53 85 Wader Chick
/way 48 43 Wild Etherwyrm
/way 57 58 Wild Etherwyrm
/way 55 34 Wild Etherwyrm

Maldraxxus
/way 30 33 Animated Cruor
/way 35 21 Animated Cruor
/way 57 36 Animated Cruor
/way 38 33 Bleak Skitterer
/way 63 33 Bleak Skitterer
/way 54 60 Bleak Skitterer
/way 58 38 Crawbat
/way 55 60 Crawbat
/way 45 51 Crawbat
/way 45 31 Necroray Spawnling
/way 67 51 Necroray Spawnling
/way 75 48 Necroray Spawnling
/way 58 50 Pulsating Maggot
/way 45 51 Pulsating Maggot
/way 36 37 Pulsating Maggot
/way 31 30 Clutch

Ardenweald
/way 43 55 Verdant Kit
/way 38 53 Verdant Kit
/way 40 59 Verdant Kit
/way 60 30 Decay Grub
/way 66 22 Decay Grub
/way 72 37 Decay Grub
/way 25 49 Gorm Rootstinger
/way 30 50 Gorm Rootstinger
/way 69 56 Gorm Rootstinger
/way 52 56 Deepwood Leaper
/way 50 68 Deepwood Leaper
/way 38 52 Deepwood Leaper
/way 51 36 Starmoth
/way 56 34 Starmoth
/way 55 61 Tranquil Wader
/way 50 57 Tranquil Wader

Revendreth
/way 60 69 Dusky Dredwing Pup
/way 50 32 Lost Soul
/way 52 76 Lost Soul
/way 56 59 Mire Creeper
/way 47 75 Rosetipped Spiderling
/way 56 55 Rosetipped Spiderling
/way 75 56 Rosetipped Spiderling
/way 63 55 Withering Creeper
/way 75 59 Withering Creeper
/way 46 68 Withering Creeper

Was able to complete in only a couple of hours, with just the Lost Soul in revendreth giving me any trouble! My only complaint is there's no reward aside from the points, but it's a minor complaint since the list is so easy to complete.