After you complete your battles throughout the game, you will build Momentum which essentially is gradual XP that you can use to upgrade the special abilities of each character. When you press the back button, you will see the character select screen which allows you to spend the accumulated Points you earned on each character.
To unlock this achievement, you will need to unlock one special ability for each character excluding Star-Lord. There is also an achievement in the game to unlock ALL special abilities for everyone.