The Secret Lives of Sheep is a short quest, with a high payout, and can be completed between 6 PM and 6 AM, but it requires your presence in Aryas Village, south from Canopus Farms.
When you get to Aryas Village, you must find Cornelia, the quest-giver, in order to trigger The Secret Lives of Sheep.
The following walkthrough refers strictly to The Secret Lives of Sheep quest and explains how to complete it.
Description: “Outside of Aryas Village, biologist Cornelia is risking her life to investigate the mating habits of wild Fuzzy Sheep. If Lightning were to shadow the sheep in her stead, she would have a better chance of fighting off the monsters and solving the mystery of the Fuzzy Sheep nesting grounds.”
Location: The Wildlands
Requirements: Complete side quest: Round ‘Em Up. Start at 6 PM, and end it before 6 AM
Rewards: 3200 Gil, Maximum HP + 120, Strength + 10, Magic + 12, Cool Glasses Adornment
The moment you enter Aryas Village, assuming that you already know Dr. Sheep (Fuzzy Search side-quest), head south and look for a path that leads to the hill close to Aryas Village.
Standing near the path you should see a woman wearing a hat. She is Cornelia and once you talk to her you will begin The Secret Lives of Sheep.
For this quest, all you have to do is to follow the flock and keep it safe from all monsters that attack it. The sheep will move towards the large structure on top of the hill, but they will be attacked by various creatures.
All of them are common beasts that shouldn’t be a problem for Lightning, since you probably fought most of them. Make sure you attack first, and stay close to the sheep.
After the flock reaches its grounds inside the structure on the hill, you have to interact with one of the sheep to trigger a cutscene that ends the quest.
Along with all corresponding rewards you will also receive a Mystery Egg.