Display All Top Child Categories / Taxonomy

maybe you have to use this

$categories=get_categories(
    array( 'parent' => $cat->cat_ID )
);

Then, in a loop, display this array because you can’t do it with an echo

foreach ($categories as $c) {
    var_dump($c);
    // what you really want instead of var_dump is something to
    // to create markup-- list items maybe, For example...
    echo '<li>'.$c->cat_name.'</li>';
}