Flowing Pandaren Spirit

Here's the routine I use. Personally, I have horrible RNG so if the Idol dies before the Elemental I tend to reset the fight.

Team Layout
Anubisath Idol: [Crush] [Sandstorm] [Deflection]
Rapana Whelk: [Ooze Touch] [Acidic Goo] [Dive]
Leveling Pet: Doesn't matter, just be sure it can survive ~700 Aquatic Damage

Battle Layout

Enter Marley
Round 1 - Sandstorm
Round 2 - Crush or Pass (Marley dives so you're going to miss)
Round 3 - Deflection
Round 4 - Crush *If this misses restart the battle before you take damage
Round 5 - Crush *If this misses restart the battle before you take damage
Round 6 - Crush
Round 7 - Call Sandstorm (You will be hit by Whirlpool but Marley should be dead)

Enter Tiptoe - If you Sandstorm to kill Marley
Round 1 - Crush
Round 2 - Crush
Round 3 - Crush
Round 4 - Crush
Round 5 - Crush
Round 6 - Tiptoe should be dead, if so continue below for Elemental if not use Sandstorm

Enter Tiptoe - Marley died before second Sandstorm
Round 1 - Deflection (To avoid Whirlpool leftover from Marley)
2 - Sandstorm
3 - Crush
4 - Crush
5 - Crush
6 - Crush
7 - Crush
Round 8 - If Tiptoe is still alive Sandstorm, if he's dead by now continue below

If You have bad RNG and Tiptoe kills your Idol, swap to Rapana Whelk and Ooze Touch until dead

Enter Water Spirit

If Idol is alive
Round 1 - Swap to Leveling pet
Round 2 - Attack
Round 3 - Switch to Idol
Round 4 - Deflection
Round 5 - Crush
Round 6 - Sandstorm (Or Crush if on cooldown)
Round 7 - Crush (or Sandstorm if off cooldown)
Round 8 - Crush (You will probably die from Whirlpool this round, if not continue Crush until you die)
Round ? - Swap to Rapana Whelk
Round ? - Dive
Round ? - Win
If for some reason Dive doesn't kill the elemental, Ooze Touch until it does.

If Idol is dead
Round 1 - Switch to Leveling pet
Round 2 - Attack
Round 3 - Switch to Rapana Whelk
Round 4 - Dive
Round 5 - Dive Hits
Until you win: Ooze Touch, if Dive comes off cooldown reuse.

1: Carry pet (should have 500HP to survive)
2: Anubisath Idol (1,1,1)
3: Emerald Proto-Whelp (2,1,1)

vs Marley
- Attack with your Carry pet > switch to Anubisath Idol
- Deflection > Sandstorm
- From here on, cast Deflection when there is 1-turn left on your Whirlpool debuff or when Marley has dived, Sandstorm when off cooldown, Crush as a filler

vs Tiptoe
- Chain cast Crush, unless your Sandstorm is off cooldown (then cast it)
- Switch to Emerald Proto-Whelp when your Anubisath Idol dies
- Emerald Bite until Tiptoe dies

vs Pandaren Water Spirit
(- If your Anubisath Idol is still alive at this point, cast Crush until it dies > switch to Emerald Proto-Whelp)
- Proto-Strike when there is 1-turn left on Whirlpool and Geyser
- Emerald Bite all the way

I just thought I'd add something I happened to stumble across while lvling the new 5.4-pets:
Chi-chi (won from the Celestial Tournament) absolutely destroys this trainer!

With the first pet, Marley, simply use alpha strike twice, go ethereal and finish it off with another alpha strike.

The second pet likewise, simply use alpha strike, it will also be dead in 3 turns.

Lastly, the elemental, is the only one worth using Wild Magic on. You also can opt for Tranquility, but you might get in trouble if you miss a single attack on the elemental. First Wild Magic, then 2 alpha strikes, untill all the time-bombs are about to go off, ethereal, continue with AS. The 2nd time the abilities won't line up, but no worries: avoid the 2nd whirlpool with ethereal, and with one more AS after that the elemental should be dead. Geyser won't be activated a 2nd time, as long as you put Wild Magic.