Note: The Skier is the only suggested character because you can only do the achievement with the Skier.
To earn it, you should start on Level N-6, not Level N-7, Touch the forward moving conveyors near the end of the last level, and the easiest set of tiles to reach for is the very first set, the ones protruding at the front. Remember that as you do it, jump at the very edge of the platform, so you can reach the first conveyors in the level.
Alternatively, you can start on Level N-7 and just play normally. You will start gaining speed due to the Skier's acceleration, and after a while, you will have enough speed to make it to the conveyors.