Preperation for this: Be sure to get Helix of the Delver staff weapon from the first Delver Echo boss that you fight in the Gideon's Rock area. Just try to cut of it's arms and the weapon should be yours in no time at all. After you have this staff weapon acquired, be sure to upgrade it when ever you can !
Now for the achievement; After a defeating Major General Ezra Shields you will trigger a major story event. For this event, proceed on as usual while fighting new enemies and exploring new areas. Once you find a certain chest in a very ambuishy type of area you will be ambushed by Delver Echo Alpha boss. Damage him to the point where you are sure that you can finish him off with the Helix of the Delver staff. DO NOT KILL IT with any other weapon than the Helix weapon. The killing blow must be dealt by the Helix of the Delver weapon.