Fetch the latest post with attachment image

This is a tricky one. If you wanted to get the latest image attachment and display the post associated with it, you could use:

$attachments = get_posts('post_type=attachment');
$first_attachment_post = get_post($attachments[0]->post_parent);

To get the latest post, but only if it has an attachment, I think the only way to do it would be with two nested queries. For example:

$the_query = new WP_Query( $args );
while ( $the_query->have_posts() ) : $the_query->the_post();

        $attachments = get_children( array('post_parent' => get_the_ID(), 'post_type' => 'attachment', 'post_mime_type' => 'image') );

        if ( $attachments ) {
            // Post output here will only be display if attachments are found
            echo '<li>' . get_the_title() . '</li>';
        }
endwhile;