This quest succeeds the invasion of the super being quest and appears after its completion. This is the second extra quest found after completing the main storyline of the second dot hack GU Reminisce game. An email will let you know when this becomes available.
You can start the quest from the quest shop on the theta server. Here you will get a chance to choose your team before heading off to the dark morrigu barrow wall (theta returning invincible huge being ). I recommend getting the best fighters in your party, these will be the ones with the most aggressive fighting styles that land several blows in a rapid manner. A decent fighter which has some healing spells would also be a plus although I set most of my party members to rage and performed the curing myself with items.
Once everything is good to go, warp to the dark morrigu barrow wall via the chaos gate to encounter the god eater, a leveled up version of the one sin (no dungeon this time). He fights in the same manner as the previous boss quest except his attacks are more lethal to your characters. This means watch out for the beam attack from the core because a single hit could lead to a progression of hits which will KO before you are able to heal. For this battle I tried to save up my beast awakenings for the core but at times I found them useful to lower the defensive shield.
Once destroyed he drops a rainbow scale which is a decent piece of armor.