Taming the World

Taming the World is a pet battles achievement earned for defeating 40 master-level pet tamers on the Eastern Kingdoms, Kalimdor, Outland, Northrend, or Pandaria continents. Upon completing, the Safari Hat is automatically added to the Toy Box.

Letter from Breanni
The hat comes attached to a letter from Breanni:

Stuck
If you're stuck at 39/40 criteria, see Audrey Burnhep as an Alliance character to get Julia, The Pet Tamer or Varzok as a Horde character for Zunta, The Pet Tamer. You don't have to be the opposing faction to complete the quest but need to be to just get the quest.

Series

 * 1) Taming the Wild
 * 2) Taming the Great Outdoors
 * 3) Taming the World