Battle Safari

I've completed Drustvar so far and have gotten 4 pets: Giant Woodworm, Coastal Scuttler, River Otter and Shack Crab all from Falconhurst. My friend managed to get a Sandyback Crawler in the same area as a secondary pet although it didn't show up for myself. My friend managed to get a rare otter - but that was the only one that ranked above common.

Having now looked through all of the pets to see what I need to collect as I zone; this is the breakdown I think they have produced for rare pets:

Kul'Tiras
Drustvar:
- [npc=143045]
- [npc=143037]

Stormsong Valley:
- [npc=143033]
- Honey Bee
- [npc=143032]
- [npc=143036]
- [npc=143031]
- [npc=143034]
- [npc=143035]

Tiragarde Sound:
- [npc=143042]
- [npc=143056]
- [npc=143041]
- [npc=143039]
- [npc=143040]

Zandalar
Zuldazar
- [npc=143044]
- [npc=143046]
- [npc=143049]
- [npc=143043]

Nazmir
- [npc=143047]
- [npc=143055]
- [npc=143057]
- [npc=143048]
- [npc=143053]
- [npc=143052]
- [npc=143054]
- [npc=143051]
- [npc=143050]

Happy Collecting!

EDIT:
Having now actually tried to catch these pets, it seems to be completely random if the 2nd/3rd pets are uncommon or not - a few times other pets have dropped as rares in different zones. It seems to be worth trying / entering a battle to see what appears. Worst case, exit the battle and then heal up your pets with bandages.

Locations of the required pets with TomTom waypoints, sorted by zone:

Pet

Zone

Comments

TomTom

[npc=143045]

Drustvar

/way Drustvar 27.59 71.27 Coastal Scuttler

[npc=143037]

Drustvar

NPCs at Falconhurst are hostile for horde players.

/way Drustvar 33 41 River Otter

[npc=143040]

Tiragarde Sound

/way Tiragarde Sound 40.52 32.36 Shack Crab

[npc=143041]

Tiragarde Sound

/way Tiragarde Sound 69.27 13.29 Inland Croaker

[npc=143039]

Tiragarde Sound

/way Tiragarde Sound 56.44 15.33 Parasitic Boarfly

[npc=143042]

Tiragarde Sound

/way Tiragarde Sound 56.22 16.33 Giant Woodworm

[npc=143056]

Tiragarde Sound

/way Tiragarde Sound 72.52 46.41 Hermit Crab

[npc=143035]

Stormsong Valley

/way Stormsong Valley 44.75 65.79 Valley Chicken

[npc=143033]

Stormsong Valley

Alongside the river.

/way Stormsong Valley 65.27 66.42 Freshwater Crawler

Honey Bee

Stormsong Valley

/way Stormsong Valley 73.54 67.86 Honey Bee

[npc=143034]

Stormsong Valley

/way Stormsong Valley 62.75 63.11 Vale Marmot

[npc=143036]

Stormsong Valley

/way Stormsong Valley 64.65 52.16 Sandyback Crawler

[npc=143032]

Stormsong Valley

/way Stormsong Valley 64.27 43.02 River Frog

[npc=143031]

Stormsong Valley

/way Stormsong Valley 70.44 31.58 Shadowback Crawler

[npc=143048]

Nazmir

/way Nazmir 38.20 83.30 Elusive Skimmer

[npc=143047]

Nazmir

/way Nazmir 29.99 67.67 Bloodfever Tarantula

[npc=143052]

Nazmir

/way Nazmir 30.47 55.62 Returned Hatchling

[npc=143051]

Nazmir

/way Nazmir 23.81 53.12 Sticky Oozeling

[npc=143053]

Nazmir

These pets have an ability called 'Burst'. This ability kills the user instantly, thus making it very hard to catch before they use that ability.
But you can check which abilities the enemy pet can use, by hovering over its potrait after engaging in a pet battle. If they have the ability 'Burst', instantly concede before attacking and reengage the pet. They will keep their rarity, but may have different abilities selected. Do this until it has the ability 'Toxic Skin' instead of 'Burst' selected.

Thanks Kurasu for the tactic in the comments of [npc=143053].

/way Nazmir 31.45 44.45 Glutted Bleeder (See notes)

[npc=143057]

Nazmir

/way Nazmir 30.99 33.71 Coastal Bounder

[npc=143050]

Nazmir

/way Nazmir 28.89 26.18 Young Sand Sifter

[npc=143054]

Nazmir

In and around The Necropolis.

/way Nazmir 36.15 26.90 Spectral Raven

[npc=143055]

Nazmir

All around Krag'Wa's Burrow.

/way Nazmir 76.23 52.26 Boghopper

[npc=143044]

Zuldazar

All around the shore of the island.

/way Zuldazar:Zandalar 59.51 80.67 Barrier Hermit

[npc=143043]

Zuldazar

/way Zuldazar:Zandalar 59.41 78.48 Shore Butterfly

[npc=143046]

Zuldazar

The road into Atal'Dazar starts at 43.98 38.48.

/way Zuldazar:Zandalar 42.40 36.34 Golden Beetle

[npc=143049]

Zuldazar

/way Zuldazar:Zandalar 71.89 28.05 Leafy Flutterwing

Waypoints:

/way Drustvar 27.59 71.27 Coastal Scuttler
/way Drustvar 33 41 River Otter

/way Tiragarde Sound 40.52 32.36 Shack Crab
/way Tiragarde Sound 69.27 13.29 Inland Croaker
/way Tiragarde Sound 56.44 15.33 Parasitic Boarfly
/way Tiragarde Sound 56.22 16.33 Giant Woodworm
/way Tiragarde Sound 72.52 46.41 Hermit Crab

/way Stormsong Valley 44.75 65.79 Valley Chicken
/way Stormsong Valley 65.27 66.42 Freshwater Crawler
/way Stormsong Valley 73.54 67.86 Honey Bee
/way Stormsong Valley 62.75 63.11 Vale Marmot
/way Stormsong Valley 64.65 52.16 Sandyback Crawler
/way Stormsong Valley 64.27 43.02 River Frog
/way Stormsong Valley 70.44 31.58 Shadowback Crawler

/way Nazmir 38.20 83.30 Elusive Skimmer
/way Nazmir 29.99 67.67 Bloodfever Tarantula
/way Nazmir 30.47 55.62 Returned Hatchling
/way Nazmir 23.81 53.12 Sticky Oozeling
/way Nazmir 31.45 44.45 Glutted Bleeder (See notes)
/way Nazmir 30.99 33.71 Coastal Bounder
/way Nazmir 28.89 26.18 Young Sand Sifter
/way Nazmir 36.15 26.90 Spectral Raven
/way Nazmir 76.23 52.26 Boghopper

/way Zuldazar:Zandalar 59.51 80.67 Barrier Hermit
/way Zuldazar:Zandalar 59.41 78.48 Shore Butterfly
/way Zuldazar:Zandalar 42.40 36.34 Golden Beetle
/way Zuldazar:Zandalar 71.89 28.05 Leafy Flutterwing

Spoiler

Waypoints using Zuldazar:Zandalar are currently bugged in TomTom. Use this in Zuldazar:
Don't use in Dazar'alor, exit the city

/way 59.51 80.67 Barrier Hermit
/way 59.41 78.48 Shore Butterfly
/way 42.40 36.34 Golden Beetle
/way 71.89 28.05 Leafy Flutterwing


The rest of the waypoints can be used like normal:


/way Drustvar 27.59 71.27 Coastal Scuttler
/way Drustvar 33 41 River Otter

/way Tiragarde Sound 40.52 32.36 Shack Crab
/way Tiragarde Sound 69.27 13.29 Inland Croaker
/way Tiragarde Sound 56.44 15.33 Parasitic Boarfly
/way Tiragarde Sound 56.22 16.33 Giant Woodworm
/way Tiragarde Sound 72.52 46.41 Hermit Crab

/way Stormsong Valley 44.75 65.79 Valley Chicken
/way Stormsong Valley 65.27 66.42 Freshwater Crawler
/way Stormsong Valley 73.54 67.86 Honey Bee
/way Stormsong Valley 62.75 63.11 Vale Marmot
/way Stormsong Valley 64.65 52.16 Sandyback Crawler
/way Stormsong Valley 64.27 43.02 River Frog
/way Stormsong Valley 70.44 31.58 Shadowback Crawler

/way Nazmir 38.20 83.30 Elusive Skimmer
/way Nazmir 29.99 67.67 Bloodfever Tarantula
/way Nazmir 30.47 55.62 Returned Hatchling
/way Nazmir 23.81 53.12 Sticky Oozeling
/way Nazmir 31.45 44.45 Glutted Bleeder (See notes)
/way Nazmir 30.99 33.71 Coastal Bounder
/way Nazmir 28.89 26.18 Young Sand Sifter
/way Nazmir 36.15 26.90 Spectral Raven
/way Nazmir 76.23 52.26 Boghopper

Notes:

• 
  
• Use the addon Paste to paste all TomTom waypoints at once.
• 
  
• Many of these pets can be found at multiple locations or as secondary pets. These are just locations i was able to find these pets at.
• 
  
• Some of this pets can also be found in Vol'dun. For ease of use i decided to just list coordinates in fives zones.
• 
  
• For more information check the corresponding page for the pet you're looking for.
• 
  

These Zuldazar Waypoints worked for me:

/way Zuldazar 59.51 80.67 Barrier Hermit
/way Zuldazar 59.41 78.48 Shore Butterfly
/way Zuldazar 42.40 36.34 Golden Beetle
/way Zuldazar 71.89 28.05 Leafy Flutterwing