An easy and short script for a smooth 2D follow camera in Unity.

SmoothCameraFollow2D.cs

using UnityEngine;

public class SmoothCameraFollow2D : MonoBehaviour
{
    public GameObject Target;
    public float LerpValue = 0.05f;

    private float _t;
    private Vector3 _pos;

    void Start()
    {
        _pos = this.transform.position;
    }

    void FixedUpdate()
    {
        if (Target != null)
        {
            _t = LerpValue;

            _pos.y = Mathf.Lerp(this.transform.position.y, Target.transform.position.y, _t);
            _pos.x = Mathf.Lerp(this.transform.position.x, Target.transform.position.x, _t);

            this.transform.position = _pos;
        }
    }
}