Making an enemy fly towards Object and then around it until it's destroyed

I would recommend using two rigidbodies(for enemy and target) and a distance joint. First i would set a velocity for gameobject to enter the area. After the gameobject is in the area (in trigger), i would set a distance joint between enemy and target. Something like:

 using UnityEngine;
 using System.Collections;
 
 public class Enemy : MonoBehaviour {
 
     public Transform target;
     private Transform thisTransform;
     private Rigidbody2D rgbody;
     public float radius = 5.0f;
     private bool connected = false;
     private DistanceJoint2D joint;
     public float InitialVelocity = 5.0f;
 
     // Use this for initialization
     void Start () {
         thisTransform = transform;
         rgbody = gameObject.GetComponent<Rigidbody2D>();
         if(target != null)
         {
             var fromGOtoTargetVec = target.position - thisTransform.position;
             var fromTargetToTangent = Quaternion.AngleAxis(90.0f, Vector3.up) * fromGOtoTargetVec.normalized * radius;
             rgbody.velocity = (target.position + fromTargetToTangent - thisTransform.position).normalized * InitialVelocity;
         }
     }
     
     // Update is called once per frame
     void FixedUpdate () {
         if(connected)
         {
             joint.distance -= .001f * Time.fixedDeltaTime; //modify this value
         }
             
     }
 
     void OntriggerStay(Collider other)
     {
         var otherRB = other.GetComponent<Rigidbody2D>();
         if(otherRB != null && !connected && (other.transform.position - thisTransform.position).magnitude < radius)
         {
             joint = gameObject.AddComponent<DistanceJoint2D>();
             joint.connectedBody = rgbody;
             joint.distance = radius;
             connected = true;
         }
     }
 }

You should set target Sphere collider as trigger.