To get this achievement you firstly need to view a replay of your race which is available after you have finished a full race (ie you've completed all of the laps...3/3 or 4/4) or view a saved replay from the "My Profile" section.
Then once the replay is playing scroll across to the make a movie tab (near the end, it is a picture of a film strip, 3rd from right) then click it and follow the onscreen instructions (basically just pressing
until it saves)... a progress bar will appear on your screen and it can take a while to save the movie.
Here's a video (Lengthy creating process is edited out)