This achievement can be kind of glitchy. Took me 3 tries to get it. You need to join an online session during the qualifying or the race and spectate the race (I'm not sure if it will pop if you spectate the practice round).
First you need to tab over to Quick Play at the main menu, then choose Browse Online. It will search for the current online games. Near the right side of each session will be a column that says, well, "session" and it has an L, P, Q, and an R for Lobby (I'm guessing), Practice, Qualifying and Race respectively. If the letters are white, that means the game session has that particular stage in it. If the letter is grayed out, it doesn't have that stage of the session in it. If it is yellow, the game session is currently in that stage.
On the far right column is the column that says which game session you are allowed to join at that moment. If you see either the Q or R in yellow (again I don't know if you can spectate practice) and it says join next to it, select that gaming session.
You will be in the lobby and others already in the session should be racing. At the bottom underneath the roster, you should see "Spectate" after everything gets done loading in. Hit spectate and it should take you to a loading screen and you will see a percentage bar at the bottom right, loading you into the race. Once it loads into the race and you are spectating someone, the achievement should pop in a few seconds.
Where it got glitchy for me was hitting the "Spectate" from the lobby it would take you the loading screen with the percentage bar but the percentage bar wouldn't be there. I was stuck on this screen but could hear the race going on and when it finally loaded, the race was over and no achievement because I never actually spectated anyone. So if it does this, just try it again.
There were only 2 or 3 sessions up when I tried for this achievement so not sure how many people are playing this game or how easy a session will be to find. Also, I did enter the lobby as it was in qualifying and ended up getting the achievement at this stage so you don't necessarily have to spectate the actual race.