The side-quest named Omega Point, available in the Wildlands area of Lightning Returns: Final Fantasy XIII, can be started as soon as you finish the second main-quest named Healing An Angel, but to finish it you have to heal the Angel of Valhalla, and learn how to glide.
Thus, before starting Omega Point, make sure that you finish A Final Cure and that the bandages around the Chocobo’s wings have been removed.
As soon as the Angel of Valhalla is fully recovered, travel to Eremite Plains, and visit the Research Camp.
To find the Research Camp, the moment you enter Eremite Plains, head east and look for the Research Leader, to start the quest explained below.
Description: “In the Wildlands is the Omega Point, the location where the Chaos first burst into the world 500 years ago. At a nearby camp, scientists conduct a research mission that most of the world has forgotten.”
Location: The Wildlands
Requirements: Complete main-quest 3-2: Healing An Angel
Rewards: 1600 Gil, Maximum HP + 80, Strength + 4, Magic + 6, Aerial Guard’s Badge Adornment
As you enter the Research Camp you can find the Research Leader on an upper platform on the right side of the main entrance. He has a brown cap and two stars above his head, indicating that he is the client you are looking for.
When you talk to him, he will ask you to find 4 units of data for him. All four units of data you have to recover are in Eremite Plains, and all of them are located on elevated platforms, meaning that you can’t get them unless you glide.
Because you don’t want to waste time looking for the missing units of data, follow the order below to get them faster. From the elevated platform where you have found the Research Leader, if you look down you should see two black structures.
On the second one is the first data unit. Glide on top of the first structure, then jump and glide on the second one to get the unit. Next, head NW and climb the largest hill. Continue to move north and on the other side of the said hill is the second data unit.
From your current location, retrace your steps and move SW. To your right is a smaller elevated area, on which you can glide to retrieve the third unit of data. On your main map, it is located on the western side of Eremite Plains.
For the final data unit, travel to the north-easternmost point in Eremite Plains where you will find the Crash Site. Dismount the Chocobo and climb the ladder that leads to the ship, then turn right and look behind the wreck for the fourth data unit.
Now, return to the Research Leader and show him the 4 units of data you have found to complete Omega Point side-quest.