A Cool Clear is when you have cleared the entire board of pegs, apart from one blue and one orange peg. The text of the achievement is a little misleading as the last blue peg will always turn into a purple hi-score peg - it still counts. Bounce your ball off the orange peg to hit the purple to complete the level to unlock this achievement.
This is easiest done in quick play mode on any of the early levels, simply pick your favourite. Try to leave a blue peg close to an orange, then proceed to carefully clear the rest of the board, focusing on getting free balls from the bucket or with high scores.
As the achievement description says, this only unlocks when you're playing a single player game mode - online or offline multiplayer doesn't work.
The video below shows an example of what your last shot will look like (credit to dowkidrock).