Calling the_content
from within attachment.php will bring you the Attachment Description.
Put the code below on your page and see what you can get from within attachment.php file:
while ( have_posts() ) : the_post();
/**
* @link https://codex.wordpress.org/Function_Reference/wp_get_attachment_metadata#Related
*/
$data = array(
get_the_ID(), // Gets att ID.
get_permalink(), // Gets att page link.
get_the_title(), // Gets att title.
get_the_content(), // Gets att description.
wp_get_attachment_metadata(), // Gets att metadata.
);
var_dump( $data );
endwhile;
Also, you might want to take a look at https://codex.wordpress.org/Function_Reference/wp_get_attachment_metadata#Related and see other functions that will perhaps be useful for you.