This quest is initiated by examining some shackles in the room with Dyrilisia in Runnyeye -80.73, 1.66, -92.15 . You must collect fabric from a good number of flags inside of Runnyeye. Click on each flag to examine them.
Known locations are:
After obtaining each of these you must return the fabric to the empty crate in the room where the quest was initiated, to the right of the empty manacles -92.06, 3.02, -96.33 .
You then need to search the bodies of the hanging evil eyes until you find an egg sac. These are two hanging evil eyes in the Chefs room 85, -16, -233 .
After examining them you must place the egg sacs in the crate that initiated the quest. Then visit the crate on the other side of that room -67.62, 0.98, -86.07 to finish the quest.
EDITOR'S NOTE: The map provided is courtesy of Sullust Organa of Steamfont.