In this quest you go through hordes and hordes of Folks in each area of the map until you get to 3 Fomoires. Don't try to defeat all the folks in any given area because they r endless and just keep on coming. On your second go through if you want to get purple dusts to say level up Automata then you can defeat/absorb a lot before defeating the Fomoires because that gives you more purple dusts at the end.
When you get to the try using your fully leveled up Formoire because it has a wide range and hits them all. Try your best to get them all to go into pink ID mode then try to keep hitting them all even if you have to hit 2 at a time then move over to the other. This keeps them all long in ID mode so they all get closer to death simultaneously. You want to do this because for each Formoire you defeat those left get stronger n the last 1 can pretty much kill you with 2 hits. When you r down to your last Formoire I say activate transcension and go at it. The final one also calls Urisk and Ulhgik so be carefull and take them out if you have to.
When thats dont move on to the lake area and get you reward.