Character Controller Rotation

You could calculate the enemy->player direction and Slerp the enemy forward to it - but the calculated direction must be strictly horizontal, or the enemy will tilt weirdly when the heights are different:

 var turnSpeed: float = 5;
 
 private var target: Transform;
 
 function OnTriggerEnter(other: Collider){
   if (other.tag == "Player"){ // player entered trigger:
     target = other.transform; // make it the target
   }
 }
 
 function OnTriggerExit(other: Collider){
   if (other.tag == "Player"){ // player exited trigger:
     target = null; // no target at sight
   }
 }
 
 function Update(){
   if (target){ // if target at sight...
     // find the target direction:
     var dir = target.position - transform.position;
     dir.y = 0; // make direction strictly horizontal
     dir.Normalize(); // normalize it
     // turn gradually to the target each frame:
     transform.forward = Vector3.Slerp(transform.forward, dir, turnSpeed * Time.deltaTime);
     // your attack code may be here:
     // -- attack code --
   }
 }

The code above may be different from what you already have - adapt the direction part to your current code, or adapt your shooting code to the script above.

EDITED: This is the C# version:

 public float turnSpeed = 5;
 
 Transform target;
 
 void OnTriggerEnter(Collider other){
   if (other.tag == "Player"){ // player entered trigger:
     target = other.transform; // make it the target
   }
 }
 
 void OnTriggerExit(Collider other){
   if (other.tag == "Player"){ // player exited trigger:
     target = null; // no target at sight
   }
 }
 
 void Update(){
   if (target){ // if target at sight...
     // find the target direction:
     Vector3 dir = target.position - transform.position;
     dir.y = 0; // make direction strictly horizontal
     dir.Normalize(); // normalize it
     // turn gradually to the target each frame:
     transform.forward = Vector3.Slerp(transform.forward, dir, turnSpeed * Time.deltaTime);
     // your attack code goes here:
     // -- attack code --
   }
 }

Notice that basically the differences are restricted to the way variables and functions are declared.