Retrieve Image from Media Library by it’s category

'category_name' will not work. You are making use of a custom taxonomy, not build-in categories. It seems from this that you have a misunderstanding about taxonomies. Please take your time and see this post on this particular subject

For custom taxonomies, use a tax_query to retrieve the posts that you need. Here is an example:

$query_images_args = array(
    'post_type' => 'attachment',
    'post_mime_type' =>'image',
    'post_status' => 'inherit',
    'posts_per_page' => -1,
    'tax_query' => array(
        array(
            'taxonomy' => 'attachment_category',
            'field'    => 'slug',
            'terms'    => 'SLUG OF YOUR TERM',
        ),
    ),
);
$query_images = new WP_Query( $query_images_args );