This achievement is actually very easy, considering that you really don't have to do anything. It just takes a lot of patience to wait until you finally reach the end. The long conveyor slows you down and makes the wait quite long (it depends on which character you use). It stretches all the way down to the end of the level so moving left and right is not required unless you want to.
This achievement can only be completed if you are in position and ready to hit the conveyors before entering this level. If your character does not touch the conveyor for the first few tiles and onward, you will not get the achievement. This may happen you can't shift around the tunnel during that small period of time between every level and align yourself with the conveyor in time. If that's the case, then you would have to wait until the next time you would come across this level in Infinite Mode.
The Runner is recommended because she moves faster on slow conveyors than most of the other characters. Characters like the Child and the Pastafarian are not recommended because they are very slow on slow conveyors, and the Bunny and the Skater cannot even complete the achievement.
A funny way to cheat the achievement is to use the Gentleman. The requirements are to not jump, touch the conveyor at least once, and not touch any other tiles. The Gentleman can fly through the whole level and land on the conveyor near the end, and still get the achievement.