void Update()
{
Vector3 prePosition = transform.position;

this.transform.position = Vector2.MoveTowards(this.transform.position, new Vector2(Player.transform.position.x, Player.transform.position.y), Speed * Time.deltaTime);

if(transform.position.x - prePosition.x >= 0){
transform.localScale.x = 1;
}else{
transform.localScale.x = -1;
}
}

こんな感じでどう?
2Dやったことないけどねw