These achievements require you to pass a certain number of checkpoints without dying. These will unlock on the way to getting the "Perfect Run/Rescue" achievements. Passing 3 and 10 checkpoints without dying is fairly easy, but 20 is quite a bit more challenging. It is best to start at Level 1 as the levels just get more and more difficult as you progress. Unlike "Perfect Run" and "Perfect Rescue," these achievements can be earned in Practice Mode, which is slightly easier considering there is no Chaser.
An easy method to unlock these, once you have all other achievements, is to reinstall the game to get your three slow motions back (WARNING: You lose all progress). You should be able to unlock this if you use three consecutive slow motions after passing 10 checkpoints without dying, getting to 20 with ease.