I just finished it...much tougher than I expected! Very fun.
The trainers weren't too bad, on my realm at least we had Lorewalker Cho, Pickles McLeary, and Dr. Ian Goldbloom. Pickles gave me the most trouble, with his undead racoon that has a critter-strong main attack and uses unholy ascension when he drops. The rabbit hit my moth for 700 (weak) with that @_@. I wish I could remember the teams I used here better but I just looked at what types they had and picked 3 hard counters until I won.
The celestials weren't bad at all. I threw 3 mechs at Xu-Fu, I think it was Tranquil Yeti/Darkmoon Tonk/Gnome (but I didn't get to the Gnome). His first move was Moonlight so having Call Lightning is a plus.
I tried to throw another 3 mechs at Zao, but because of his Wish, I used the Beast of Fable team of Unborn Valk/Water Spirit/Chrominius. My timing was off on Curse of Doom and it hit one turn before Geyser/Whirlwpool, but the combo still got him and seemed to ignore the "Boss Defense: May not deal more than 35% of their heal with one attack". That seems to be like the Magic Racial, so multi-hit moves are nice there.
Yu'la I used Idol with Smash/Stoneskin/Deflection, which got it down to roughly 35%. I then brought in a Kun-Lai Runt and Shatter-combo'd my way to an easy win.
For Chi-Chi, I noticed that he had an attack/dodge/hot, so I figured he'd be a giant pain in the ass. I used my 2nd valk (only level 19) and my Water Spirit/Chrom from Zao's fight (Spirit at 70% hp~, Chrom at 100%). I did Curse->Haunt(didn't have UA unlocked), and then the standard combo. I should mention that Chi-Chi killed Chrom the turn I had planned to use Surge of Power, but the combo killed Chi anyway.
All in all I think I used maybe 14 pets in all.
Very fun tournament! I wish everyone else good luck
I like your style better than that of the guy further up the list that was quoted from the forums.
I didn't think the three "undercard" fights were too bad. If you play up advantage types you should do fairly well. Most difficult one I had was Pickles, because Socks is a critter death machine. Ended up starting with a frog there and did rather well.
As for the title fights:
Yu'la seems the easiest. You can almost solo it with a Gregarious Grell. Adding an Anubisath Idol to the team made it a cake walk. I didn't even need whatever pet was in third position (which was for me was a Peddlefeet, just in case I needed the big humanoid shot through the heart).
For Chi-Chi, I used the Beast of Fable team of Unborn/Water Spirit/Chrominius. Noticed something odd. Unholy Ascension seems to kill undead flat out now, or at least it did for me. Didn't notice that change in the patch notes. So I threw curse of doom first, then UA, and then followed the normal pattern. I think Chrom needed to make a single attack to knock off the last 60 hp or so, but it was stunned so it wasn't that much of an issue.
I had some minor luck with an Unholy Ascension/Call Darkness/Nocturnal Strike team on Zao, but I think the one time it worked it was mostly luck. The easiest method I ran across was pure Zandalari Cheese. Black Claw/Hunting Party. I had to switch in a Kneebiter when the Anklerender went down, but Zao dropped before he got his wish.
Xu-fu is I think the hardest to do. I too went with Yeti/Gnome/Tonk. A lot more switching between pets in the middle of the fight than I normally do. I think, in the end, I got lucky with a stun from the Tonk's Shock and Awe just when I really needed it. Of all the fights, this is the one I'm going to keep watch on to see if someone finds a better strategy for.