The Fox/Spider/Mechanical strat works pretty good in most cases. The only way this will fail is if Niuzao gets a crit on your first pet.
Against Niuzao:
Fox/Crystal Spider/Darkmoon tonk (or Tranquil Mechanical Yeti)
Moves: Dance, Bite, Howl, Brittle Webbing, Spiderling Swarm, Crystal Prison (switch to mechanical) Ion Cannon if in range (check the damage in the tooltip and divide by 2), otherwise filler>Ion Cannon
Same tactic works for Xu-Fu as well.
Alternative tactic:
Pandaren Water Spirit/Chrominius/Darkmoon Tonk (Or Yeti)
Geyser, Whirlpool (switch to chrominius) Howl (switch to tonk/yeti) if in kill range with Ion Cannon, use it. Otherwise use filler into an Ion Cannon.
The comments on wowhead on each of the pets/trainers in the tournament are also full of great advice. Usually there's multiple strategies with easy to acquire pets. A lot of those strategies are almost fool-proof and generally don't even fall over to RNG.
It's been a long time for me since i did it, but i just killed Xuen with Call Lightning (ruby dragon hatchling?) and then the good old turrets from the Clockwork Gnome
Niuzao I did with the "cheat mode" combo: Whirlpool, Chrominius Howl + Surge of Power