The main trick to it seems to start with a pet that has Ion Cannon
and to use that on the first round. The first pet is going to get swapped out after that round anyway, so the recharge isn't a problem. What you do after that shouldn't matter too much, because you just took out a third of his health in the first round.
That first Ion Cannon really doesn't hit that hard because of the 50% reduction buff. Sure it's possible to power through him by just pounding away at him but almost all strats I've seen use some technique to work around the buff instead of just powering through it.
Howl/Hunting Party/what ever takes that 50% reduction and flips it up to a 50% increase. So the 1000 point Ion Cannon that gets reduced to 500 by the buff gets pushed up to 1500 by the debuff. That means two rounds of big attacks with the debuff up take a huge chuck out of his health. Shock and Awe + Ion Cannon with the debuff up should be enough to almost kill him.
% health abilities like Trample and explode ignore the 50% reduction buff so continue to hit pretty well. This means a DM Zep exploding ends up hitting as hard as an Ion Cannon with no debuff up.
Multi-hit abilities combined with + X amount of dmg debuffs also adds a huge amount of extra dmg. Black Claw + batter or Turrent is pretty crazy dmg. Using the strat against Aki results in 1k+ dmg in a single turn which still hurts through the 50% reduction buff.
My preferred strat uses two of the three and he's a complete joke. I open with Ion Cannon and let him swap out that pet into a Direhorn who tramples until almost dead and then Stamped's so that the 100% debuff is up for a mech to blow him to pieces but by that point almost any mech would do as he's already softened up and the mechs are hitting so hard.
There are a number of other pets you could use instead of the Direhorn and several of them would probably even work better if you didn't have any good mechanical units. Clefthoof runts, Peanut and the Pint-Sized Pink Pachyderm all have both Trample and Stamped like the direhorn. They even have Survival which would be good for an extra attack since you are faster. Give me two random mechs and any one of those pets and you should be able to win easily. Just have to make sure your second mech has less health than your Direhorn/peanut.