The Gym Rat badge is an unlockable badge in which you will get +4 to your Speed, Acceleration, Vertical, Strength, and Stamina. It can be unlocked through the following methods:
On Current Gen: The easiest way to get it is to play a full season of MyCareer (at least 55 regular season games) and win a championship. Doing so will unlock the badge only on the player you win the championship with.
On Next Gen: You will get a Quest to talk to the Gatorade Rep. This will unlock the mission to get the Gym Rat badge, which includes 50 3-star exercises. This can be accomplished quicker by completing the Gatorade Reaction Drill.