Well, one form of cheating is elucidated in the scenario's backstory: misrepresenting oneself (or selves): the former contestants who had been disqualified in an earlier competition had impersonated each other so that they were always "fresh" for a contest.
The other way would be use of resources exterior to a match *during* the match: for example, in the Boar and Tiger exhibition, if the PC who decides to represent his team were helped or buffed by teammates before or during the match, that would be construed as cheating.
Using outside help for the whole team to prep for a match would also be cheating (like convincing another wizard, cleric etc. to cast long-term buffs on the party prior to entering a challenge, that sort of thing).
There might also be things the crowd won't like, but which really aren't "cheating"; for example, in the cliffside challenge, a PC using flight obviously might not be cheating (if it's his spell, shoes, potion etc, or that of his team), but clearly that violates the spirit of the match, undermines its fun value for the crowd, and should impose penalties on the team's combat performance checks.
The basic idea here is that the spectators want a *good show*, and they don't like things which are maybe *too* quick and effective, because what fun is that?
I forsee one of the PC's doing the breaking test wildshaped... thats why I asked
That wouldn't really be cheating, it's using their natural abilities. No real difference between that and a barbarian raging before trying to break something.
Really the big no-nos for the PCs are using outside help, leaving the island, killing those who yield, and looting the bodies of fallen foes. Other than that it's just a question of honor and fairness. The tournament is put on by the church of Abadar and they have some strict ideas about that.
There's a lot of things they can do that might make the crowd grumble. Pretty much anything that is outside the "spirit" of the challenge could fall into this category. Remember that one of the rules is that the Emissary must be obeyed at all times and his word is final. So if a competitor is "breaking" a challenge feel free to have the Emissary step in.
And as mentioned if you are using performance combat the crowd will boo anything they don't like, forcing a check.
Oh, and a side note that may make some groups want to cheat: