Break the sound barrier.
You break the sound barrier (and earn the X-1 Medal in the top left corner of your screen) by either, using your rocket booster or pulse booster by pressing immediately after you get hit with a soundwave or getting hit with the Soundwave while you are in the middle of using the above boosters. This will most likely unlock as you play through the career but if it doesn't then it is possible in party mode offline with 2 controllers, though it's tricky to do solo. Your best bet if it hasn't unlocked on its own is to play the later career races and watch out for the other racers who pick up the soundwave and boost as they shoot you. The acceleration of your vehicle doesn't matter for this, it can be done in any vehicle.