Get the title and URL of the attachment parent post

All attachments has got a post parent which you can access with $post->post_parent inside the loop or get_queried_object()->post_parent outside the loop on your image.php or similar single post pages. (See my question here and the answer by @gmazzap why you should rather avoid $post outside the loop)

Now that you have the post parent ID, it is easy to rewrite your function: (CAVEAT: Untested)

function get_parent_post_anchor()
{
    /*
     * Make sure we are on an attachment page, else bail and return false
     */ 
    if ( !is_attachment() )
        return false;

    /*
     * Get current attachment object
     */
    $current_attachment = get_queried_object();

    /*
     * Get the permalink of the parent
     */
    $permalink = get_permalink( $current_attachment->post_parent );

    /*
     * Get the parent title
     */
    $parent_title = get_post( $current_attachment->post_parent )->post_title;

    /*
     * Build the link
     */
    $link = '<a href="' . $permalink  . '"  title="' . $parent_title . '">' . $parent_title . '</a>';

    return $link;
}

You can then use it as follow

echo get_parent_post_anchor();