Sorting Tags by Slug Value

You can set orderby slug like :

$tags = get_tags( 'order=ASC&orderby=slug' );

$html="<div class="post_tags">";
foreach ( $tags as $tag ) {
    $tag_link = get_tag_link( $tag->term_id );

    $html .= "<a href="https://wordpress.stackexchange.com/questions/340357/{$tag_link}" title="{$tag->name} Tag" class="{$tag->slug}">";
    $html .= "{$tag->name}</a>";
}
$html .= '</div>';
echo $html;