Triggering a Player Hit Animation

 bool playerHit = false;
 if (playerHit && collision.gameObject.tag == "Enemy"){
 animator.SetTrigger ("Hit");

You are setting playerHit to false, so the following if-statement will never execute.

Do you need the playerHit variable? If this script is on your player, then the fact that the OnCollisionEnter2D method is executing is enough to know that your player got "hit" by something. It seems counter-intuitive to set playerHit to false there. You should be fine by removing the

  bool playerHit = false;

line, and changing the if-statement to

 if (collision.gameObject.tag == "Enemy")
    animator.SetTrigger ("Hit");

Another simple fix is to just set 'playerHit' to true:

 bool playerHit = true;

It would make more sense to set it to true rather than false, but the variable is still redundant if you're not using it someplace else

UPDATE:

That can't be your entire method, because you're missing a couple of ending brackets. I'm going to assume this is how your code is structured (and I added comments):

 void OnCollisionEnter2D(Collision2D collision){
             bool damagePlayer = false;
 
             // Collision with enemy
             EnemyScript enemy = collision.gameObject.GetComponent<EnemyScript> ();
              /* You shouldn't do this, because if the gameobject you're colliding with doesn't have
              * the EnemyScript, this line will create a runtime exception. Since you're checking for
              * null in the following if-statement, I think it works, but it's not the best way to do it */
 
             if (enemy != null) {
 
                 // Damage the player
                  /* Your method runs line by line from top to bottom. Since you are setting damagePlayer
                  * to false at the start of the method (and you don't change it after that), the following
                  * if-statement will never be true, so that whole block will never execute */
                 if (damagePlayer) // This is always false {
                     HealthScript playerHealth = this.GetComponent<HealthScript> (); // This will never execute
 
                     if (playerHealth != null)    // Nor will this
                         playerHealth.Damage (1);// Nor that
                 }
                 
                 if (collision.gameObject.tag == "Enemy") {
                     animator.SetTrigger ("Hit");
                 }
             }
 }

Wont the following method suffice?

 void OnCollisionEnter2D(Collision2D collision)
         {
             if (collision.gameObject.tag == "Enemy") // If colliding with enemy, execute this block
             {
                 HealthScript playerHealth = this.GetComponent<HealthScript> ();
                 playerHealth.Damage (1);
                 animator.SetTrigger ("Hit");
             }
         }