How did you add this image alt text.
WP stores alt text added when editing an image in the media folder to the meta key of _wp_attachment_image_alt so this will work to retrieve it
$alt = get_post_meta($attachment_id, '_wp_attachment_image_alt', true);
But if you added alt text through some other means then it could be stored in some other way. Please explain further how the alt text was added if this is the case.
