You have two options:
Ranked Championships, which is the regular online mp found in the main menu.
Ultimate Championship, which is the UT online mp found in UFC Ultimate Team menu.
I suggest doing regular online (ranked) and choose the best fighter for the weight class you prefer to fight in. Just win 4 times in a row, and the achievement is yours.
As for fighting, you don't need to be a pro, but you do need some skill and strategy. Keep your distance, don't forget to use body shots (majority just cover their heads). Take your time, do not rush your opponent or you will get Jose Aldo'd. Not every punch or kick has to be a haymaker (lb).