Those four tamers represent the elements of Pandaria: Fire, Water, Earth and Air.
Similar to the pet trainers, once you beat them in an initial quest, they offer a daily with a satchel that can contain the pet version of the Spirit Tamers:
Pandaren Fire Spirit
Pandaren Water Spirit
Pandaren Earth Spirit
Pandaren Air Spirit
Those are some nice looking pets and the Pandaren Water Spirit
has a special place in our hearts. He was one of the most important pets in most collections because of the famous "Howl-Bomb" strategy, which however was made impossible in patch 7.0.3.
Below you will find a list of pets that are suitable to beat all four spirit tamers. You do not necessarily need those pets, but with them you can use the first alternative listed here on every fight:
The list of required pets can sadly not be displayed right now due to updates Blizzard is making on the armory.
A new version of the tables will be added as soon as possible.