It'll be interesting to see if the Plushie has to survive each fight to get each tick of the achievement. Otherwise, you'd just need a two-pet strat for each, and let the Plushie die at the start of each fight. That seems unlikely, though -- I'm guessing it'll need to survive.
LeCraft's tweet said they'd be adding more battles to that achieve, but just the Celestials could be kind of tricky under the current tourney format. If you lose any of the four fights, you'd have to (a) have backup teams ready, (b) start the event from the beginning, or (c) do it over several weeks. Curious to see if there'll be any reward other than a couple of ach points.
At least two of the Celestials shouldn't be too bad, if the current strats hold up in 6.0. There are several two-pet strats for Yula, and Zao usually dies to Call Lightning combined with any Zandalari pet with Hunting Party. Xufu is still RNGish for me with three pets, tho.
I'm in the beta, so I plan to tinker with this sometime during the week, assuming it doesn't crash long enough for me to get out to Timeless Isle.
Maybe an aoe attack where it throws itself off the other team like a rubber ball or bean bag. Or maybe a two round attack that's like 'aw, so kewt' that lures the other pet into dropping its defense and then it would bit it when it got too close or something. 
