This achievement requires you to unlock all rewards for a single fight in the 'Ultimate Fights Mode'. Just pick a fight within the class you are most comfortable with (if you like striking, pick one from 'Ultimate Knockouts' and if you like grappling choose one from 'Ultimate Submissions'), check the requirements for a class-challenge and meet the requirements during a fight. Meet all the requirements for 3 challenges for both fighters, so 6 challenges in total for the same match and the achievement is yours.
This doesn't have to be done in one or two fights. Once a challenge is unlocked, it is saved and you can fight the same fight as many times as you require to obtain all challenges.