Go to 'Infinity'
Then go to 'War Games'. This is the competitive multiplayer mode.
Choose any game type; you can accrue five wins over time, they don't have to be in a row or in one sitting. If you're new to the game, I recommend Big Team Infinity Slayer, as you'll have less 1 on 1 combat than other modes.
A lot of people have had problems with when this is unlocking. Several sources have confirmed that you need to play the game from start to finish in order for the win to register. That means if you quit, or join mid-game, it won't count as a win. Check your 'Service Record' and then check the 'War Games' section to see how many "wins" you have accrued.