Taming Kalimdor

Going through the quest line which starts with Varzok, one will encounter the following trainers in chronological order:

Zunta, for the quest Zunta, The Pet Tamer is located in Durotar. Coords: 44, 28
Pets (lvl 2, Common):
Critter (Mumtar) - use Beast
Beast (Spike - use Mechanical

Dagra the Fierce, for the quest Dagra the Fierce is located in Northern Barrens. Coords: 58, 53
Pets (lvl 3, Common):
Beast (Longneck, Ripper) - use Mechanical
Critter (Springtail) - use Beast

Analynn, for the quest Analynn is located in Ashenvale. Coords: 20, 29
Pets (lvl 5, Common):
Flying (Flutterby) - use Magic
Aquatic (Mister Pinch) - use Flying
Critter (Oozer) - use Beast

Zonya the Sadist, for the quest Zonya the Sadist is located in Stonetalon Mountains. Coords: 59, 71
Pets (lvl 7, Common):
Beast (Acidous, Constrictor) - use Mechanical
Critter (Odoron) - use Beast

Merda Stronghoof, for the quest Merda Stronghoof is located in Desolace. Coords: 57, 45
Pets (lvl 9, Common):
Elemental (Ambershell) - use Aquatic
Aquatic (Bounder) - use Flying
Critter (Rockhide) - use Beast

Cassandra Kaboom, for the quest Cassandra Kaboom is located in Southern Barrens. Coords: 39, 79
Pets (lvl 11 - Uncommon Elite):
Mechanical (Cluckatron, Gizmo, Whirls) - use Elemental

After defeating Cassandra Kaboom, you get the quest A Tamer's Homecoming. The completion of this unlocks both Battle Pet Tamers: Eastern Kingdoms and Battle Pet Tamers: Kalimdor.

As this is the page for Taming Kalimdor, I will present the tamers met throughout Battle Pet Tamers: Kalimdor.

Traitor Gluk is located in Feralas. Coords: 59, 49
Pets (lvl 11-13, Uncommon):
Dragonkin (Glimmer) - use Humanoid
Critter (Prancer) - use Beast
Beast (Rasp) - use Mechanical

Grazzle the Great is located in Dustwallow Marsh (Silly wowhead. Not in Theramore's Fall!). Coords: 53, 74
Pets (lvl 14, Uncommon):
Dragonkin (Blaze, Firetooth, Flameclaw) - use Humanoid

Kela Grimtotem is located in Thousand Needles. Coords: 31, 32
Pets (lvl 15, Uncommon):
Beast (Cho'guana) - use Mechanical
Critter (Indigon, Plague) - use Beast

Zoltan is located in Felwood. Coords: 40, 56
Pets (lvl 16, Uncommon):
Magic (Beamer, Ultramus) - use Dragonkin
Mechanical (Hatewalker) - use Elemental

Elena Flutterfly is located in Moonglade. Coords: 46, 60
Pets (lvl 17, Uncommon):
Magic (Beacon) - use Dragonkin
Flying (Lacewing) - use Magic
Dragonkin (Willow) - use Humanoid

The follow-up from Battle Pet Tamers: Kalimdor is Grand Master Trixxy, where one has to defeat Stone Cold Trixxy whom is located in Winterspring. Coords: 65, 64
Pets (lvl 19, Uncommon Elite):
Flying (Blizzy) - use Magic
Beast (Frostmaw) - use Mechanical
Dragonkin (Tinygos) - use Humanoid

Congrats on your achievement!

for those who use tomtom

/way Durotar 44, 28 Zunta (Pets lvl 2)
/way Northern Barrens 58, 53 Dagra the Fierce (Pets lvl 3)
/way Ashenvale 20, 29 Analynn (Pets lvl 5)
/way Stonetalon Mountains 59, 71 Zonya the Sadist (Pets lvl 7)
/way Desolace 57, 45 Merda Stronghoof (Pets lvl 9)
/way Barrens 39, 79 Cassandra Kaboom (Pets lvl 11 - elite)
/way Feralas 60, 50 Traitor Gluk (Pets lvl 11-13)
/way Dustwallow Marsh 53, 74 Grazzle the Great (Pets lvl 14)
/way Thousand Needles 32, 33 Kela Grimtotem (Pets lvl 15)
/way Felwood 40, 56 Zoltan (Pets lvl 16)
/way Moonglade 46, 60 Elena Flutterfly (Pets lvl 17)
/way Winterspring 65, 64 Grand Master Trixxy (Pets lvl 19 - elite)

Tnxs foor the coord kkjaatun

A Tip for everyone who wants to do this, but wants the bag on an alliance char.
You can accept the quest at an horde char, then log onto your alliance char and defeat the tamer.
You can turn in the quest and get the bag.