This achievement requires you to "String it" for every movie scene in the game. That is 36 full combos.
The two things that you will use the most to keep your string going are drifts and near misses.
Each level is a driving map with stunts laid out, but if you watch carefully it's also laid out with objects at the furthest 2 seconds away from eachother. What you will want to do is find the path that lets you drive close to each object so that a near miss keeps your string going. If you find there are no objects but you are in an open enough area or see a turn coming up, drift. If you are on a bike, instead of trying to drift when you have no objects nearby, you can do a wheelie.
Keep in mind that you are allowed to miss some of the stunts and still get 5 stars, as long as a reshoot of the scene is not called for. If you find going for a stunt repeatedly causes you to lose your streak, don't bother doing it. For less practiced stuntmen this is often the case for 180 Reverses.