When driving around some tracks you will see a line of red dots. You will need to drift this line to collect all of the dots. Once you collect every one of the dots you get the trophy. Sometimes one of the dots will go gray for no real reason. If this happens the game has determined that you weren't properly drifting and you wont get the trophy for this. Its pretty simple to get this and you are bound to get it eventually.
Execute a perfect drift line