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: You will need to complete the Mamba Mentality quest first, but afterwards you will need to talk to the NPC in front of the Gatorade Facility. He will give you a quest.
The “Addicted to Sweat” quest requires you to complete 50 exercises in the gym. You can also win a championship for your MyCareer team while playing 50+ games and get the Gym Rat Badge.
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 25 3-star exercises. This should take at least 5 weeks to unlock.