The Trials are accessible on the right side of the Main Menu of Killer Instinct. Their purpose is to suggest a challenge or what-to-do-next-idea for the gamer.
You can attain this Xbox Achievement also while only just playing a few Dojo Lessons of Killer Instinct, but you can take on any challenge of the Trials you wish. Definitely you attain this Xbox Achievement by playing Killer Instinct in any way you desire, very soon and without any stress of special focus, with barely an effort.
Killer Instinct refers to trails on two different things. It also rarely refers to it as being the challenges that await you inside Dojo Lessons.