need help with enemy script

The problem is that, while you were changing 'moveDirection' in an attempt to lower the player's Y co-ordinate value, 'moveDirection' itself was not being used, and therefore had no effect.

The same method of creating gravity is found on the Unity Scripting API under 'CharacterController.Move'. However, this method uses a character controller to put 'moveDirection' to use.

Here is a link to the aforesaid page on the Scripting API: http://docs.unity3d.com/ScriptReference/CharacterController.Move.html

I have edited the script so that it uses a character controller (which I attached to the player) to create the effect of gravity:

 var target : Transform; //the enemy's target
 var moveSpeed = 3; //move speed
 var rotationSpeed = 3; //speed of turning
 var gravity = 20.0;
 var Lives = 3;
 private var dead = false;
 
 private var moveDirection : Vector3 = Vector3.zero;
 
 var myTransform : Transform; //current transform data of this enemy
 
 function OnMouseDown()
 { 
     if(OnMouseDown)
     { 
         Dead = true;
         Lives -= 1;
     }
     print(Lives);
 }
 
 function Awake()
 { 
     myTransform = transform; //cache transform data for easy access/preformance
 }
 
 function Start()
 {
     target = GameObject.FindWithTag("Player").transform; //target the player
 }
 
 function Update ()
 { 
     var controller : CharacterController = GetComponent.<CharacterController>();
 
     //rotate to look at the player 
     myTransform.rotation = Quaternion.Slerp(myTransform.rotation, Quaternion.LookRotation(target.position - myTransform.position), rotationSpeed * Time.deltaTime);
 
     //move towards the player
     myTransform.position += myTransform.forward * moveSpeed * Time.deltaTime;
 
     //Apply gravity
     moveDirection.y -= gravity * Time.deltaTime;
 
     switch(Lives)
     {
         case 0:
             Destroy(gameObject);
             break;
     }
 
     controller.Move(moveDirection * Time.deltaTime);
 }

Please inform me if you encounter problems using this edition of your script.