Jeremy Feasel

Here is my 2 pet strategy it hasn't failed on me yet.

Slot 1 Mechanical pandaren Dragonling: 1-2-2
Slot 2 lDarkmoon tonk 1-1-2
Slot 3 Leveling pet / Elekk Plushie

Start of with the Mechanical pandaren dragonling (I am assuming the pets you use are level 25 with the exception of the leveling pet ofcourse)

Judgement
1: Thunderbolt
2: breath until judgement is dead

Honky Tonk
1: Decoy
Thunderbolt on cooldown and Breath until Honky-Tonk is dead

Once your dragonling dies bring in your leveling pet and imediately switch over to your darkmoon tonk (no action from your leveling pet required)

If your dragonling dies before Honky-Tonk is dead a misile from your darkmoon tonk will finish him off.

Fezwick
1: Shock and Awe
2: Ion Canon

You should be done now :)

My heart stopped when I saw this NPC, I know this doesn't mean anything to anyone, but My uncle was killed in 2013 in an accident and his name was Jeremy "James" Feazell.

Seeing this npc brought back a lot of fond memories.

EDIT: This strat is more accessible now that Molten Corgi is available through the anniversary vendor. However, I'd really recommend the DragonsAfterDark strat on Xu-Fu , which uses the same 2 pets, remarkably, for BOTH Darkmoon challenges.

Fast, reliable 2-pet strategy seeing as the Dragonling / Tonk strat is proving unpredictable. This one depends on allowing Dragonling to use Decoy against Judgement, allowing it to retire and then come back and use the decoy against Fezwick later. The second pet (if you have it...) also has an immune.

1. Mechanical Pandaren Dragonling 1.2.2. (Flame / Thunderbolt / Decoy)
2. Molten Corgi 2.2.1 (Flamethrower / Cauterize / Puppies of the Flame)
3. Level Pet

Start with Dragonling.
1. Decoy
2. Thunderbolt (edit: You can just spam Flame as well, but this may result in Dragonling not dying to Fezwick and getting less XP for level pet).
3. Flame til Judgement dies.
Bring in Molten Corgi. This is the round that may be susceptible to RNG, ie when or if the Honky-Tonk deploys a stun. But the Corgi is faster than the Honky-Tonk.
1. Puppies of Flame.
2. Flamethrower
Then Cauterize if you take a hit from the laser, or Flamethrower on CD until the mechanical dies.
Enter the monkey. Swap in level pet to soak the stun.
Bring in Mechanical Pandaren Dragonling.
1. Decoy.
2. Thunderbolt
3. Flame til Dragonling dies.
Bring in Corgi.
1. Puppies of Flame and Flamethrower to finish off the monkey.
End.

EDIT: If you don't have the Molten Corgi then the widely-available Autumnal Sproutling can step in with Lash / Nature's Ward / Sons of the Root. Try to ensure Nature's Ward is up prior to using Sons of the Root.