The hierarchy for custom taxonomies is:
taxonomy-$taxonomy-$term.php
taxonomy-$taxonomy.php
taxonomy.php
archive.php
index.php
So, if your taxonomy was called cats, you could target that specific taxonomy with a template file taxonomy-cats.php.
If you wanted to style your tabby cats differently than the rest (because of course you would), then you could use taxonomy-cats-tabby.php.
See wphierarchy.com