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Direbeak hatchling (Swarm, ironskin, predatory strike) could solo the first two pets.

After that, switch to nexus whelping to get rid of sandstorm with Arcane Storm and Mana Surge until dead.

You're going against a critter, beast, flying team so plan accordingly.

Personally, I used a (H/S) Menagerie Custodian, a (P/P) Zandalari Kneebiter, and a (P/P) Jade Oozeling. I just did their main talents until things died.

Edit: I've switched my team a bit and have some instructions in the form of a Rematch team.

The new team is a (P/P) 221 Zandalari Kneebiter, an (H/S) 112 Menagerie Custodian, and an (S/S) 221 Nether Farie Dragon. The following paste is for Rematch.

Talia Sparkbrow:4AP2:221814S:112916B:2215HD:N:Turn 1) Black Claw\nTurn 2) Leap\nTurn 3-4) Hunting Party \n\n>Eighty Eight Dead\n\nSwitch to Menagerie Custodian\n\nTurn 5) Shock and Awe\nTurn 6) Zap\nTurn 7) IF at this time the failsafe has activated, use Ion Cannon. If not, use Zap until failsafe is used or Turbo is dead\n\n>Turbo Dead\n\nSwitch to Nether Farie Dragon\n\nTurn 8) Arcane Blast until Cocoon Strike hits (Usually after Sandstorm)\nTurn 9) Moonfire\nTurn 10) If below half health, use Life Exchange, otherwise Arcane Blast\n \nContinue these until dead

I used Iron Starlette (1, 1, 1), a low level pet to get some experience and Sprite Darter Hatchling (2, 1, 1) for this...worked first time. Credit to Phacoid from Xu-Fu Pet Battle Strategy Guide for this strategy.