You will need a Chocobo in the Calm Lands to do this Sidequest. Once you have it, head to the beginning of the Calm Lands and you’ll need to go to the bottom right corner of the map to find a Chocobo Feather on the ground. Press the X Button in front of it to be transported in a secret area, press Circle to get down of your Chocobo and head up to find a secret temple.
You will be in Remiem Temple, go examine the sphere to the left of the Temple to learn more about the races in Remiem Temple, then go to the right of the Temple and examine the chocobo to race on a track under the temple. Win the race to win the Cloudy Mirror. You will then have a message telling you to activate it. Head to Macalania Woods, South. Find the little boy and his mother near a save point there. Save your game if you want and pick the Jecht Sphere near the little boy if you want. Now, from the save point, go right and don’t turn left on the next screen, continue up and on the next screen, go up. Speak to the man there and tell him his wife/boy are waiting for him. Return to the first Save Sphere and talk to the mother and father of the little boy TWO TIMES EACH. If you don’t speak to them two times, a woman will be blocking the path. Next, go up at the intersection, near the Save Sphere. Continue up until you meet a boy standing in front of a large crystal. Speak to the boy and use your Cloudy Mirror in front of the crystal. You will obtain the Celestial Mirror, the key to obtain all of your Legendary Weapons.