Convert imploded plain text into links

<?php
$categories = get_field('categories');
$elements = array();
foreach($categories as $category) {
    //do something
    $elements[] = '<a href="' . $url . '" title="' . $title . '">' . $name .'</a>';
}
echo implode(',', $elements);
?>

at the //do something here you should find what the URL should be for your category/tag

something like get_tag_link() might be of use.

Also have you looked at using the_tags() It does what your after and can be used in the loop.