To obtain this achievement you must be an Xbox Live friend and a RaceNet friend and rival of the player you want to beat.
To add a friend on RaceNet search his RaceNet username*
in the search bar in the upper right of the page, then once you click on the username you have to send him a friend request clicking on the button on the lower right of the page.*Note that the RaceNet name isn't always the GamerTag of your friend, so ask him to log in onto RaceNet and make him tell you his username and accept the request.
As said on the above solution by oG II GiiFT3D, go to https://racenet.codemasters.com/grid2/rivals
to add a rival, click on the +
sign under a social tab and send a request to the desired friend.
Once your friend accept the rival request start the game and go to Multiplayer, Xbox Live and then Rivals, here you should see your friend under social, this means you've followed all the steps and you're right.Your friend need to be online to play with you (obviously), don't worry if you can't race him on the rivals page, this isn't needed.
Instead create a custom match or join a playlist or whatever you want to play with your friend, once you win the achievement should pop.
I've done it with a playlist, i won the first race and the achievement popped up, then i let my friend win the second race and the achievement popped also for him.
Sorry for my bad english, if there is something you can't understand please send me a message or write a comment.
Also please don't ask for a partner in the comments, instead create a boosting session, if you need help you can send me a message with the session link and i'll join if i can.