Hide Image Container if No Image Attachments

You need to add the query before the actualy displaying of the div, then you can run your conditional. According to get_posts() it returns an array, so I’m assuming it returns an empty array if posts aren’t found, thus we can check is it’s not ! empty()

<?php $args = array( 
        'post_type' => 'attachment', 
        'orderby' => 'menu_order', 
        'order' => 'ASC', 
        'post_mime_type' => 'image',
        'post_status' => null, 
        'numberposts' => null, 
        'post_parent' => $post->ID 
    );

    $attachments = get_posts( $args );
    if( ! empty( $attachments ) ) :
?>
    <ul id="slider" class="exhibit-slide">

        <?php foreach ( $attachments as $attachment ) {
            $alt = get_post_meta($attachment->ID, '_wp_attachment_image_alt', true);
            $image_title = $attachment->post_title;
            $caption = $attachment->post_excerpt;
            $description = $attachment->post_content;
        ?>  

            <li>
                <div class="exhibit">
                    <img src="https://wordpress.stackexchange.com/questions/181683/<?php echo wp_get_attachment_url($attachment->ID); ?>" alt="<?php echo $alt; ?>">
                </div>
            </li>

        <?php } ?>
    </ul>
<?php endif; ?>