Get Off My Lawn

The Viturak Cabal are one of the minor factions, and they have a home planet like any other faction. Bomb the home planet to eradicate their colony and they are effectively killed off (even if there are some straggler ships around the systems afterwards).

If you haven't already, max out reputation with them first for We Are Here To Stay before destroying their world (doing this has no bearing on your ability to destroy them).

If, after maxxing reputation, you're unable to attack then select their homeworld and in advanced planet options (bottom-right corner) there's an action to break the truce with them (permanently!). Do this and after a 30-seconds-ish wait you'll be at war immediately.

Also, it has to be you that destroys them; if another faction does so you don't get the achievement. Hence this is soft-missable.