Once you’ve completed the initial set of battles, the next level of Battle Pet Tamers will become available from Varzok in Orgrimmar. You can fight these characters in a pet battle for increased XP, achievements and rewards. The quest is account-wide but faction specific.
Defeating each one will give you a 5min Pet Recovery debuff, meaning you’ll have to wait out the 5min before you can battle another Battle Pet Tamer.
The five you will need to defeat in Kalimdor are:
Traitor Gluk <Master Pet Tamer>
Location: On the right side of main path heading into Dire Maul
Level 13 Pets: Prancer (Critter), Glimmer (Flying) and Rasp (Beast)
Grazzle the Great <Master Pet Tamer>
Location: Dustwallow Marsh – To the left of Ony’s Lair
Level 14 Pets: Blaze, Flameclaw and Firetooth (3x Dragonkin)
Kela Grimtotem <Master Pet Tamer>
Location: Thousand Needles – On a mesa, NW of Darkcloud Pinnacle
Level 15 Pets: Plague (Critter), Indigon (Critter) and Cho’guana (Beast)
Zoltan <Master Pet Tamer>
Location: Felwood – Just off the main path towards Jaedanar
Level 16 Pets: Beamer (Magic), Ultramus (Mechanical), Hatewalker (Mechanical)
Elena Flutterfly <Master Pet Tamer>
Location: Moonglade – By the lake (side of the flight masters)
Level 17 Pets: Beacon (Magic), Lacewing (Flying), Willow (Dragonkin)
Completing this chain, opens up the quest to defeat the Grand Master of Kalimdor.
Stone Cold Trixxy <Grand Master Pet Tamer>
Location: Winterspring – Ice Thistle Hills, by old ruins
Level 19 Elite Pets: Blizzy (Flying), Tinygos (Dragonkin) and Frostmaw (Beast)
Defeating the Grand Master on each continent will unlock daily quests (via an achievement) for all of the other Tamers on that same continent (10 shots a day if you do them all).
Completing this chain allows access to the Outland series of battles.