I saw a forum post stating some confusion over this achievement and after unlocking it last night I wanted to share the method I used.
A friend and I went into separate Time Trial events with the same car(doesn't matter the model, just make sure you are both using the same.) Make a small adjustment on your tune and save it under setups and all tracks. Name it whatever you wish. We finished the event to make sure a time was recorded with the tune.
When the above step is done create a private online match. You will need to share the tune at the pre-race screen. To get there you will need to add a practice round before the actual race. Make sure both of you are in the same car you used for the Time Trial, go over to share, select the tune, then your friend and share. After a few seconds the achievement popped for both of us.
A couple of bullet points to this:
-You do not need to actually do the race you setup in the online lobby.
-Creating a match with just a race and no practice or qualifying will lead you straight to the track so make sure these options are turned on to ensure the pre-race screen.
-We had it set for ONE AI opponent as well.
-An obvious one, but the person will need to be on your friends list.
EDIT: As per rob25x, you may need to remove each other as friends and re-add one another through the lobby system in them game and then share the tune. A console restart after removing a friend may be necessary.