2D Diablo style movement

Try using this script as your player controller. This works in my 2d game. I found it in the following tutorial Click To Move in Unity 5. The example he creates in the tut is for 3d but it worked for my 2d game. Good luck and hope this helps!

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 
 [DisallowMultipleComponent]
 public class ClickToMove : MonoBehaviour 
 {
 
     [SerializeField] [Range(1,20)]
     private float moveSpeed = 5;
 
     private Vector3 targetPosition;
     private bool isMoving;
 
 
     // Use this for initialization
     void Start () 
     {
         targetPosition = transform.position;
         isMoving = false;
     }
     
     // Update is called once per frame
     void Update () 
     {
         if(Input.GetMouseButton(0))
         {
             SetTargetPosition ();
         }
 
         if(isMoving)
         {
             MovePlayer ();
         }
 
     }
 
     void SetTargetPosition()
     {
         targetPosition = Camera.main.ScreenToWorldPoint (Input.mousePosition);
         targetPosition.z = transform.position.z;
         isMoving = true;
     }
 
     void MovePlayer()
     {
         transform.rotation = Quaternion.LookRotation (Vector3.forward, targetPosition - transform.position);
         transform.position = Vector3.MoveTowards (transform.position, targetPosition, moveSpeed * Time.deltaTime);
         if(transform.position == targetPosition)
         {
             isMoving = false;
         }
 
     }
 }