This is a tricky achievement.
Right as the level starts, don't move forward or to the sides at all. Use the button that makes Doodle grab your tail, and then go and find each gatestone piece. Try not to move after getting them, because even the slightest slither can invalidate the achievement. After Doodle finished the gatestone grab animation, grab your tail again and move on to the next one. Repeat this for every piece, and the achievement will pop up after completing the level.