The Generic Quest is a hidden "quest" occurring after the Main Quest is complete, which involves collecting four generic items: Generic Stone, Generic Ice, Generic Water, and Generic Fire. Collecting all four will award the "Generic Quest" achievement. The items can only be obtained in a specific order, which can be done with the following five steps:
Enter the Sunken Ruins, and open a chest on Floor 1 containing Generic Stone.
The description of Generic Stone reads, "A rare stone that has an engraving of a spoon. I wonder what it means." This hints that Fork is the next destination, since a spoon and a fork are a colloquial pair.
The description of Generic Ice reads, "An ice cube that never melts. Looks like a frozen heavenly material." This hints that Landing is the next destination, since the cube's being "heavenly" clues that it must have come from Aurora Island (which Lina quotes "is the place where you can touch the sky"), and Landing is where the ice cube must have fallen.
Go to Smalltown (or any other town in the Flash Version) and accept the quest "Lake Trouble".
(The description of Generic Water reads, "A flask of pure fresh water. I think it might come from a lake somewhere." This hints that Lake is the next destination.)