Pirate Hunter

Pirates don't spread too far (1 jump) from their homeworld, so you'll know you're close when you start seeing pirate ships. Bomb the homeworld to destroy their colony and this will unlock.

See There Can Be Only One - and be sure to max the relationship with the Pirates first for Talk Like A Pirate before destroying 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.

It is also soft-missable as if you play as TEC Primacy and research "Truce Amongst Rogues" then you become unable to return to being at war with them and hence cannot kill them off.