> If you could give a better explanation of what you want it would be easier to help..
> Would putting the enemy on a layer with 0,0 parallax and having it move on it's own be what you are looking for?
My enemy doesn't move like this but let's say the enemy moves up and down . The enemy should keep moving up and down it should keep moving up and down but it shall always be on screen. Basically the enemy should always be on screen.
Without better explanation it is hard to guess what you want..
The enemy won't move if you don't give it a movement behaviour (or code the movement yourself)
You could put it on a layer with paralax 0,0 to keep it on screen , clamp it to the viewport or a certain distance from the player end there are more options..
How free would the movement of the enemy be?