Advertisement challenges are infomercial type contests that appear in between certain blueprints during Shows.
There are a total of 9 advertisement challenges in the game (2 in Show 1, 2 in Show 2, 2 in Show 3, and 3 in Show 4). Please note that the Supermarket minigame does not count as an advertisement challenge.
First off, you are given an option to skip the advertisement challenges, but obviously you don't want to unless you have already beaten the challenge previously.
Next, you just have to follow the in-game trainer's instructions to pass. There are 3 different trainer types (strength, speed, and balance). Aside from the balance challenges, they are ridiculously easy.
You can get the achievement by playing the Easy Shows alone, as the ones in Hard mode don't count as separate challenges.