Cymre Brightblade

95% Winrate with a lvl 1 carry pet.

Anubisath Idol (1,1,1)
Mechanical Dragonling (1,2,2)
Carry Pet

vs Idol of Decay

1. Deflection (unless he is around 200 hp, then he casts Dark Rebirth, so just pass, once he has cast rebirth, prepare to Deflection) to block Rot
2. Sandstorm on CD
3. Crush as filler (unless you will kill him with dark rebirth up). Once his dark rebirth has worn off, just crush him until he is dead.

vs Wishbright Lantern

1. Cast Deflection if it is up, else use sandstorm.
2. Cast sandstorm if up, else just start spamming crush until your idol or he is dead, keep sandstorm on CD
3. Once your idol dies, bring in your carry pet, then instantly switch to Mechanical dragonling

4. hopefully one or 2 breaths will kill him, save thunderbolt and decoy for the last guy

vs Gyrexle

1. Cast Decoy
2. cast thunderbolt
3. cast breath until you can thunderbolt him again(he might heal, just keep going)
4. Cast breath until he dies

EDIT: Tried to explain how to avoid the dark rebirth mechanic a bit better. ~11/15/2015~

I've been using Anubis + Dragonling combo for a long time but always wanted to try something a little bit quicker and different.

I've tested it on patch 7.0.3 and it works

Came up with party which was earlier mentioned here by altimius (on 30/11/2014). Unfortunatelly he hasn't explained exacly how to go with the fight so I will instead.

Team:
1) Any Rabbit or Hare (all of them have the abilities that are needed and those which change doesn't matter for this particular fight), breed s/s, each has stats of 1400/227/357. Spells: (1/2/2) Scratch/Dodge/Stampede.
2) Mechanical Pandaren Dragonling Spells: (1/2/2) Breath, Thunderbolt, Decoy.
3) Carry pet/Elekk Plushie

Idol of Decay

Turns 1-4: Start with Rabbit/Hare and use Dodge (for Idol's Rot) and follow up with Stampede.
Turn 5: Use Scratch (you will get hit by rot)
Problem: Scratch can crit which may lead to lossing the battle.
Turns 6-7: Swap for your carry pet/Elekk Plushie and then swap again for Rabbit/Hare (you will get hit for 117 dmg from Swarm of Flies with your carry pet, a bit more if it's humanoid which i haven't tested unfortunatelly yet). Also Idol of Decay will use Dark Rebirth on this turn which you completly ignore.
Turn 8: Use Scratch, that will trigger Idol's Undead passive.
Turn 9: Use Dodge, which will make you avoid 2nd Rot hit. Note that Swarm of Flies dmg is lowered here by 25% due to 7.0.3 changes. Idol dies, Cymre will summon Wishbright Lantern. Your critter will be close to dying, ~60hp.
Problem: If Swarm of Flies crits in turn 8 and turn 9 your critter will die, which will lose you the battle.

Wishbright Lantern

Turn 10: Use Stampede. Critter dies but before that, it applies Double Damage debuff to Lantern. It works perfectly since you won't be preventing Lantern from keeping Sunny Day weather. Summon Dragonling.
Turn 11-12 max 13: Spam Breath until Lantern dies, Gyrexle enters.

Gyrexle, the Eternal Mechanic

Turn 13: Use Thunderbolt.
Problem: Gyrexle can crit with Railgun which can cause to lossing the battle.
Turns 14-15: Breath, Gyrexle will use Repair (don't worry :) ).
Turn 16: Decoy, Gyrexle will heal.
Turns 17-18: Breath, Decoy will block Railgun hit.
Turn 19: Thunderbolt, Decoy will block Rocket hit, also Sunny Day is no longer at this turn (or next one if you had to use 3 turns to kill Lantern).
Turns 20-21: Breath. On turn 21 Gyrexle will use Railgun causing your Dragonling's death and triggering his passive.
Turn 22: Breath. Gyrexle will use Repair.
Turn 23: Breath, Gyrexle dies.

Let me know if you find any difficulties while using this.

Here's a guide to using two easy-to-obtain pets to defeat this team. Using this method, you can carry low-level pets and power level them.

You will need a level 25 [npc=68659] and a level 25 [npc=64899]. The third pet must have at least 500 HP (or be a Mechanical or Magic) for this strategy to work.

Here is the setup you want to run:
Slot 1 - [npc=68659] : [petability=406] | [petability=453] | [petability=490]
Slot 2 - [npc=64899] : [petability=115] | [petability=779] | [petability=334]
Slot 3 - [Carried Pet]

Enemy Team Summary
[npc=83839] : [petability=476] | [petability=232] | [petability=794]
[npc=83836] : [petability=460] | [petability=421] | [petability=273]
[npc=82407] : [petability=712] | [petability=278] | [petability=293]

Strategy
This fight is about optimizing your turns to counter any abilities of the opposing teams. It takes some anticipation, as the opponents turns may vary, but I believe it's possible to predict any outcome!

Idol of Decay
Idol of Decay starts with using [petability=476], and subsequently every time it is off cooldown, (except when low in health, as I'll explain below) then spams [petability=232] the rest of the time. If using this strategy you somehow get hit with [petability=476], it's best to restart, as you will likely not be able to win.

PART A
If Idol of Decay is above 300 HP: Use [petability=490] for turn 1 to avoid [petability=476], and then after this every time it is off cooldown use [petability=490] again. On turn 2 use [petability=453], but DO NOT use it again against the Idol of Decay, as it needs to be up for Wishbright Lantern. Use [petability=406] as your filler ability.

PART B
If Idol of Decay has dropped below 300 HP OR you have just triggered the [petability=242] passive by killing him:
If [petability=490] is off cooldown (and you would normally use it to avoid [petability=476]), use [petability=406] instead, as Idol of Decay is going to use [petability=794]. On the NEXT turn after [petability=794], the Idol of Decay will use [petability=476], which you simply avoid with [petability=490]. If he doesn't use [petability=476]. keeping hitting him with [petability=406] until he does.
If [petability=490] is still on cooldown when the Idol of Decay drops below 300 HP, simply refer to PART A and proceed as usual.

NOTE: It is OK if [petability=794] triggers and Idol of Decay heals up. Follow the PART A strategy and he will be dead soon.

Wishbright Lantern
You will want to whittle down Wishbright Lantern with your Anubisath Idol. Eventually, Wishbright Lantern will kill your Anubisath Idol, though.

Wishbright Lantern will use [petability=460] on turn 1, which is why you need to have [petability=453] off cooldown to change the weather back.
If [petability=490] is available (off cooldown), use it on turn 1 to avoid [petability=460] damage. Otherwise, use [petability=453] on turn 1 (as you will go second). Use [petability=453] every time it is off cooldown from now on.

Use [petability=490] whenever it is of cooldown, EXCEPT on turn 5 (and 10, 15, etc.) - use [petability=453] OR [petability=406], as this turn Wishbright Lantern will use [petability=273]. Every other turn, use [petability=490] OR [petability=453], with [petability=406] as a filler.

Once your Anubisath Idol dies, bring out your Mechanical Pandaren Dragonling.

Start with [petability=334]. Next use [petability=779], then finally [petability=115] as a filler till the Wishbright Lantern is dead.

Gyrexle, the Eternal Mechanic
When Gyrexle comes out, switch for your low level pet (who will take 1 round of [petability=712], hence needs to have at least 500 HP to be guaranteed to survive). After the low level pet attacks once, switch back to your dragonling. Continue to use [petability=334], then [petability=779] when off cooldown, and [petability=115] as filler until Gyrexle is dead!

There you have it!