Try this.

It's untested, but basically I have made a few additions to your code which (along with the comments) should be fairly self-explanatory. Basically I'm using three different numeric "threshold" variables against which the current distance to the target is checked. These are used to switch between the 'chasing' and 'not chasing' state.

Also, within the chasing state code, there's now an attack clause which checks the time to make sure it only occurs once every certain time period (defined in the initial variables).

var target : Transform; //the enemy's target
var moveSpeed = 3; //move speed
var rotationSpeed = 3; //speed of turning
var attackThreshold = 3; // distance within which to attack
var chaseThreshold = 10; // distance within which to start chasing
var giveUpThreshold = 20; // distance beyond which AI gives up
var attackRepeatTime = 1; // delay between attacks when within range

private var chasing = false;
private var attackTime = Time.time;

var myTransform : Transform; //current transform data of this enemy

function Awake()
{
    myTransform = transform; //cache transform data for easy access/preformance
}

function Start()
{
     target = GameObject.FindWithTag("Player").transform; //target the player
}

function Update () {

    // check distance to target every frame:
    var distance = (target.position - myTransform.position).magnitude;

    if (chasing) {

        //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;

        // give up, if too far away from target:
        if (distance > giveUpThreshold) {
            chasing = false;
        }

        // attack, if close enough, and if time is OK:
        if (distance < attackThreshold && Time.time > attackTime) {
            // Attack! (call whatever attack function you like here)
            attackTime = Time.time + attackRepeatTime;
        }

    } else {
        // not currently chasing.

        // start chasing if target comes close enough
        if (distance < chaseThreshold) {
            chasing = true;
        }
    }
}

If you can't get it to work, or have any other questions, ask as a comment below!

@cidermodder This link might help you with the health bar part. It's a 3 part written tutorial. I hope it helps.