Target all images that are not the first attachment

I’m just modifying your code please check. Hope it will help.

<?php $args = array( 'post_type' => 'attachment',
        'numberposts' => -1,
        'post_status' => null,
        'post_parent' => $post->ID,
        'order' => 'ASC' );
     $i = 0;
$attachments = get_posts($args);
    if ($attachments) {

            foreach ( $attachments as $attachment ) {
                  if($i != 0){
                   $class="fantome";
                 }else{ $class="";}  
              $imgarr = wp_get_attachment_image_src($attachment->ID,'full');
             /*---------------this will output your image and class------- */
              echo '<img class="'.$class.'" src="'.$imgarr[0].'" />';
             $i++;
            }
    }

    ?>