Check of the object is in the screen.
Give him custom movement.
Check if Follower.X > Followed.X,
If it is, set its horizontal speed to eg. 3
Else, set its horizontal speed to eg. -3
Check if Follower.Y > Followed.Y,
If it is, set its vertical speed to eg. 3
Else, set its vertical speed to eg. -3
To make him stop when near the followed.
Check if distance(follower.Y,0,followed.Y,0) is NOT < eg. 50 when doing the above events.