I guess I'll give a complete breakdown.
Remember those black treasure chests you may or may not have opened (such as in Garocchia Forest)? They contain the Devil's Arms, rare weapons sought by the person named Abyssion.
First, obtain the Evil Eye from Toize Valley Mine.
Then find Abyssion, the dark-haired guy on the steps of a building in Flanoir, near the entrance and Inn. If someone in your party is missing, such as Colette, Abyssion might not show up.
Abyssion will give you Nebilim's Key, allowing you to open the black chests and collect the Devil's Arms. One weapon is in Sylverant, while the rest are in Tethealla and Welgaia, 9 weapons in all, including the Evil Eye.
When you've found them all, Abyssion will tell you where to meet him, then you all "do stuff." And the quest is done.