The key for this achievement is the phrase 'while it attempted to escape'. You do NOT unlock this if you kill the ruler on the same turn as it summons the pink portal. What you need to do is to kill it with an Overwatch shot or Bladestorm stroke while it is actually running towards the portal.
The easiest two are obviously the Viper King and the Berserker Queen. You can combine this achievement with 'Regicide' (kill a ruler the first time you encounter it), but this is not recommended. Ideally, you should whittle down the ruler's health for one or two encounters, so that when it does choose to escape, it'll have low enough health to easily finish off.
To increase your chances, carry a frost bomb or two into missions where you're expecting a ruler to appear. Stasis-capable Psi Ops work as well. When you've done enough damage to the ruler, it will summon the pink escape portal. Freeze/Stasis the ruler now, you should get two or three moves to put a couple of your best Overwatch guys ready. Shotgun-focused Rangers and Specialists with the Guardian skill are ideal.
Also note that this achievement becomes easier to complete the later in the game you complete the 'Alien Nest' mission. So don't hurry on that, wait for at least Magnetic Weapons, or even Plasma, before letting the rulers loose. The mission will not expire on you.