Use get_the_tags instead of the_tags to grab an array of tags, and array_chunk to split it. You will then need to build a loop to display the tags.
$tags = get_the_tags();
if (!empty($tags)) {
$tags = array_chunk($tags,ceil(count($tags)/2),true);
foreach($tags as $v) {
echo '<ul>';
foreach ($v as $tag) {
echo '<li><a href="'.get_tag_link($tag->term_id).'">' . $tag->name . '</a></li>';
}
echo '</ul>';
}
}