Spirit Tamers

There are a lot of combinations of pets you can use to beat the spirit tamers; some rely more on the random numbers coming out in your favor than others.  These are some of the combinations I've had decent luck with.

Thundering Pandaren Spirit:

• Critter: Mr. Wiggles or a Tolai Hare.  Mr. Wiggles has the health and a hard-hitting attack to survive and pummel the Pandaren Earth Spirit, and the Tolai Hare just as the speed to ignore the crowd control and usually dodge enough to get the job done.
• Beast or Dragon:  Mr. Grubbs or the Infinite Whelpling.  I've had good luck with both beating the critter-family ooze.  Set up Mr. Grubbs with Leap to flip the speed advantage and you'll get to hit hard twice in a row.  (In the screenshot, the Cinder Kitten is filling in for Mr. Grubbs.  Adorably.)
• Mechanical:  Mechanical Squirrel or Fluxfire Feline.  Really, anything with Wind-Up is going to get the job done.  Stone Rush is going to hit hard, so something that can get back up afterwards helps.

Whispering Pandaren Spirit:

• Critter: Mr. Wiggles again.  The moth can be taken out by a lot of things, but Mr. Wiggles seems to be surviving best right now of what I've got available.  It's a critter-classed moth, rather than a flyer.
• Dragon:  Infinite Whelpling.  The dragon pet does mostly air attacks, which are weak against dragons, and the Infinite Whelpling generally hits hard, especially when going second, and can heal if needed.
• Dragon or Magic:  If the Infinite Whelpling didn't survive the dragon for some reason, the Disgusting Oozeling or another dragon (Silver Dragonhawk Hatchling, etc.) can finish off the Air Spirit.

Flowing Pandaren Spirit:

• Dragon: Silver Dragonhawk Hatchling.  Quills is strong against the fish, even if you don't get to go first.
• Critter or Beast:  I've found Mr. Wiggles to be quite nice with his combination of Headbutt and Crouch.  Hoof is a solid filler attack.
• Dragon:  Infinite Whelpling.  A solid closer in most cases, the Infinite Whelpling will have few problems with the Water Spirit.

Burning Pandaren Spirit:

• Critter:  Mr. Wiggles.  The Fire Spirit gives me the the most trouble still, but I've been going with Mr. Wiggles, against whom his attacks are weak.  Headbutt plus a self-heal make a decent combination here.
• Dragon:  Infinite Whelpling.  The Infinite Whelpling can handle the dragon pet here without many problems.  Just know that the dragon will do Lift-Off after Cyclone, so don't waste a cooldown skill on that round.
• Magic:  Disgusting Oozeling.  The Disgusting Oozeling puts flying pets to shame.

There are other pet combinations that will work, but with a half a dozen pets, you can comfortably cover all four.