Get attachments by user

Use a custom query for this.

$user_id = 1;
$the_query = new WP_Query( array( 'post_type' => 'attachment', 'post_status' => 'inherit', 'author' => $user_id) );
if ( $the_query->have_posts() ) while ( $the_query->have_posts() ) : $the_query->the_post();
   the_title();
endwhile;

This will show all the attachment titles for user with user id 1. You can use get_the_ID() in the loop to get the attachment ID.