You can unlock this achievement easily (and obviously) by playing through the Season 1: Drukhari DLC.
Not so obviously, you can also unlock this achievement without ever playing the Drukhari DLC. Simply play Tarot missions, which you need to do for another achievement anyway, and many times the mission will be populated with Dark Eldar enemies. With 5 or 6 such Tarot missions, you should get enough Dark Eldar kills to unlock this.
Also, if you have the City of Suffering DLC you can unlock this achievement in no time as you will always get Drukhari enemies in these missions. Note that you must first unlock the Triglav subsector before you can access the City of Suffering DLC, which requires a power level of 1300, I believe.
Occasionally you will also face Drukhari enemies when playing random Priority Assignments.