There are 8 pet battle trainers in the Khaz Algar lands, 2 for each area. We will be going into their location, team and your best team to defeat the trainer with. None of the pet battle trainers pets will be tameable.
I would highly recommend using the Rematch addon (see guide here) to save your teams, so you don’t have to find the pets every time you want to battle a trainer. I will also include a Rematch String for every team in case you have the addon.

Isle of Dorn – Pet Battle World Quests

Awakened Custodian

Location

The location of the Awakened Custodian battle trainer is /way 48.17 31.95

Enemy Team

The Awakened Custodian opponent team consists of one Mechanical pet. It’s attacks are:

This enemy will usually start off by using Amplify Magic, and then Shock and Awe, so do not use an important ability on the second round.

Your Team

The best and fastest team to counter this opponent consists of one level 25 Unborn Val’kyr and one level 25 Ikky or Foulfeather. The last pet can be whatever pet you want, as it will usually not ever be in active combat with the enemy. Sadly, this third pet will not gain any exp from passively being in the fight. If you want to get the Battle on Khaz Algar use a full team of level 25, even the ones that are passive. Your team’s abilities should be as following:

The most effective move order is:

1. Curse of Doom
2. Haunt (reset if stunned)
3. Black Claw
4. Flock

Collector Dyna

Location

The location of the Collector Dyna battle trainer is /way 38.33 78.82

Enemy Team

Collector Dyna’s team consists of three elemental pets: Ridge, Stratus and Tiny Cragling. Their attacks are:

Your Team

The best and fastest team to counter this opponent consists of one level 25 Puddle Terror, and any pet with the Water Jet or Surge ability. I am using a River Otter. You can potentially fill your third pet spot with another Water Jet/Surge pet but it should only be necessary if you get really unlucky. Your team’s abilities should be as following:

The most effective move order is:

1. Sunlight
2. Nature’s Ward
3. Water Jet
4. Repeat

Use Sunlight off cooldown and always keep Nature’s Ward up. Clean up with the second pet, if necessary.
Credit to goatcasual on Wowhead for a very consistent team.

The Ringing Deeps – Pet Battle World Quests

Friendhaver Grem

Location

The location of the Friendhaver Grem battle trainer is /way 61.58 37.61

Enemy Team

Friendhaver Grem’s team consists of one beast pet and two critter pets: Rufus, Bubs, and Takey-Take. Their attacks are:

Your Team

The best and fastest team to counter this opponent consists of one level 25 Iron Starlette, one level 25 Zandalari Kneebiter or Zandalari Anklerender, and one level 25 Twilight Clutch-Sister or Twilight Whelpling. Your team’s abilities should be as following:

The most effective move order is:

1. Wind-Up
2. Supercharge
3. Wind-up
4. Toxic Smoke (until Iron Starlette dies)
5. Black Claw
6. Hunting Party 
7. Bloodfang 
8. Twilight Fire 
9. Twilight Meteorite
10. Twilight Fire

Haywire Servobot

Location

The location of the Haywire Servobot battle trainer is /way 66.85 58.09

Enemy Team

The Haywire Servobot team consists of one Mechanical pet. It’s attacks are:

Your Team

The best and fastest team to counter this opponent consists of one level 25 Unborn Val’kyr and one level 25 Ikky or Foulfeather. The last pet can be whatever pet you want, as it will usually not enter combat with the enemy. If you want to get the Battle on Khaz Algar use a full team of level 25. Your team’s abilities should be as following:

The most effective move order is:

1. Curse of Doom
2. Haunt 
3. Black Claw
4. Flock

Hallowfall – Pet Battle World Quests

Guttergunk

Location

The location of the Guttergunk battle trainer is /way 61.07 68.99

Enemy Team

The Guttergunk team consists of one elemental pet. It’s attacks are:

My Team

The best and fastest team to counter this opponent consists of one level 25 Unborn Val’kyr and one level 25 Ikky or Foulfeather. The last pet can be whatever pet you want, as it will usually not enter combat with the enemy, however if unlucky enough it might happen. Therefore choose a level 22 or above for the third pet. If you want to get the Battle on Khaz Algar use a full team of level 25. Your team’s abilities should be as following:

The most effective move order is:

1. Curse of Doom
2. Haunt
3. Black Claw
4. Flock

Kyrie

Location

The location of the Kyrie battle trainer is /way 52.43 62.79

Enemy Team

Kyrie’s team consists of one flying pet, one beast pet, and one mechanical pet: Flicker, Sir Pounce, and Mini Airship. Their attacks are:

My Team

The best and fastest team to counter this opponent consists of one level 25 Nexus Whelpling, one level 25 Twilight Clutch-Sister. The last pet can be whatever pet you want, as it will usually not enter combat with the enemy, however if unlucky enough it might happen. Therefore choose a level 22 or above for the third pet. If you want to get the Battle on Khaz Algar use a full team of level 25. Your team’s abilities should be as following:

The most effective move order is:

1. Arcane Storm
2. Mana Surge (if DODGE not up)
3. Arcane Storm
4. Mana Surge 
5. Twilight Fire 
6. Twilight Meteorite 
7. Twilight Fire
8. Phase Shift 
9. Twilight Fire

Azj-Kahet – Pet Battle World Quests

In Azj-Kahet you’ll only be able to see the world quests, when you’ve picked a pact with the Forge a Pact weekly quest. You pick the quest up from Y’tekhi at /way 55.2 41.2 in Azj-Kahet.

Zaedu

Location

The location of the Zaedu battle trainer is /way 53.10 31.60

Enemy Team

Zaedu’s team consists of one beast pet (itself). It’s attacks are:

My Team

The best and fastest team to counter this opponent consists of one level 25 Ikky or Foulfeather, and one level 25 Zandalari Kneebiter or Zandalari Anklerender.The last pet can be whatever pet you want, as it will usually not enter combat with the enemy. If you want to get the Battle on Khaz Algar use a full team of level 25. Your team’s abilities should be as following:

The most effective move order is:

1. Black Claw
2. Flock
3. Black Claw
4. Hunting Party

Ziriak

Location

The location of the Ziriak battle trainer is /way 61.29 36.97 in City of Threads.

Enemy Team

Ziriak’s team consists of one undead pet, one beast pet, and one flying: Tickler, Four-Legs, and Swoopgrasp. Their attacks are:

My Team

The best and fastest team to counter this opponent consists of one level 25 Rabbit, I am using Elfin Rabbit, and one level 25 Nexus Whelpling or Stormborne Whelpling. The last pet can be whatever pet you want, as it will usually not enter combat with the enemy. If you want to get the Battle on Khaz Algar use a full team of level 25. Your team’s abilities should be as following:

The most effective move order is:

1. Dodge 
2. Flurry 
3. Burrow
4. Flurry
5. Dodge
6. Flurry until Tickler dies – Dodge & Burrow off CD
7. Arcane Storm 
8. Mana Surge

Thank you so so much for reading! I hope this helps conquer the pet battling world and will bring some justice for Tom. Consider becoming a Gaming Hero member HERE to gain access to 300+ guides, which includes gold, alt and profession guides! Check out more Gaming Hero guides by CLICKING HERE!!