There is not a quest called "Echoes of Oryx".
For this achievement you must complete the 3 quests in the Taken War quest line for Earth, Venus, and Mars. These open up after the main story. The Mars quest will happen after either Earth or Venus quest is complete and is a little longer.
After those 3 missions, you must complete the mission "The Road to Kings Fall" which takes place in the raid. You will have to kill the bosses that are in the raid. Not just Oryx.