*Glitch update--11-7-19 It appears this achievement is also buggy, like all the others in this DLC! They may have broken it more with the update that was supposed to fix things! Check the comments for what's going on, this is ridiculous.*
This is currently glitched in a good way!
You only have to do ONE of the two Fragment missions with 3 runes attuned and the other one can be done with no runes.
Red Dragon Knight is in the Fragment Expedition(Githyanki)
Neothelid is in the Fragment Expedition(Illithid)
I solo'd everything up to the Red Dragon Knight mission, when he spawned I realized I maybe made a mistake starting the mission without any runes and without a group.
Killed the Red Dragon Knight... then went out, found a group for the Fragment Expedition(Illithid), went in with 3 runes, killed it and got the achievement for both.
Just for the info:
You do Reconnaissance quests for both enemy faction to unlock Warden Expeditions.
Then you do the Warden Expedition for both factions to get a Stardock Rod Section from each.
Once you have 3 Stardock Rod Sections from each faction, you can now do a Fragment Expedition for both factions.