Query Posts to fetch Posts with Unique Tag

<?php
$arg = array('cat' => '1','showposts' => 10,'offset' => 0);
query_posts($arg);
if (have_posts()) : while (have_posts()) : the_post();
?>
<a class="post-link" title="<?php the_title(); ?>" href="https://wordpress.stackexchange.com/questions/55868/<?php the_permalink(); ?>"><?php the_title(); ?></a>
<?php
if (!$used_tags) $used_tags = array();
$posttags = get_the_tags();
if ($posttags) {
    foreach ($posttags as $tag) {
        if ( !in_array($tag->term_id, $used_tags) ) {
            array_push($used_tags, $tag->term_id);
            echo '<a class="tag-link" href="'.get_tag_link($tag->term_id).'">#'.$tag->name.'</a>';
            break 2;
        }
    }
}
?>

Not tested though!