In the show 'Unbeatable Banzuke' the unicycle challenge is often called "Like a Peirrot." What is a Peirrot and why do challengers have to be like one on a unicycle?

I have not seen the show, but I am guessing you mean "Pierrot", which is a stock character in French theater. He is depicted as a clumsy clown, oblivious to his surroundings, always falling in love and always the victim of pranks and yet always maintaining his lightheartedness. On stage, he always manages to stumble and fall and if he juggles balls, they always end up on the floor.
So, in the show that you mentioned, I imagine that the person wearing the loose clown clothing of a Pierrot and made to ride a unicycle would be stumbling and falling off the unicycle, or more likely be caused to do so by some sabotage or obstacle strewn across his way --- exactly the way Pierrot is depicted on the French stage.

https://en.wikipedia.org/wiki/Pierrot
https://en.wikipedia.org/wiki/Clown#Pierrot.2FPirouette

The challenge was indeed called "Like a Pierrot" and was an obstacle course in which competitors had to ride a unicycle. They wear shorts and a t-shirt, though, not the traditional, loose Pierrot clothing. Unbeatable Banzuke is a weekly Japanese programme and the Japanese word for clown is "pierrot", so I'd say the antics refer to clowning rather than the traditional Pierrot figure described in the first reply.

https://en.wikipedia.org/wiki/Pierrot