This achievement can be completed using either the Child or the Ghost. Simply follow the path of blacked-out tiles to the end in Low-Power Tunnel, part 5. However, this is easier said than done, and you may take several tries to complete it. Try to memorize the path of tiles at the end of the level while you still have light.
Another strategy is to play the level backward. To play a level backwards, you need to go to the pause menu and press and hold the previous level button. Make sure you have beaten the next level before you do this. When you do this, you will start at the very end of the level. There are two spawn points and the only one makes it possible to not jump. There will be light as you start, and as the tunnel goes dark, you will still have an easy time getting this achievement because there is a giant patch of power tiles.