Now that you have the Celestial Mirror, you can start collecting weapons and Sigils. Let's get cracking!
Find the Caladbolg in the northwestern corner of the Calm Lands. Look for a monk standing in front of a ledge heading down. To persuade him to leave, you must complete the four stages of Chocobo training here in the Calm Lands.
Return to the path when you've fully trained a Chocobo; the monk should be gone. Continue down the path.
Use the Celestial Mirror on the device on the wall. This will open it and reveal the Caladbolg.
Obtain the Sun Crest in the same room where you fight Yunalesca, in the Dome in Zanarkand. You'll have to go up and down the stairs two times to retrieve it. Find it on the left-hand side, hidden along the wall. Don't worry--you can always return if you miss it.
Obtain the Sun Sigil by beating the Chocobo Trainer in a race with a time of better than 0:0:0. Accomplishing this requires you to avoid all the birds, hit 16 balloons and still win the race. For every bird that hits you, you must grab another balloon. Avoiding the birds in the final stretch is tough, but it can be done. Keep trying until you succeed.
Grab as many balloons in the beginning stretch as you can. This is the easiest place to shoot for balloons since there are no birds flying after you and it is relatively easy to get ahead of the trainer. Worry more about birds and balloons; chances are the trainer will soak a good number of bird strikes, and will only win maybe 1 in 20 races.
Try to stick to the right in the opening stretch, where the most balloons seem to spawn and where they are easiest to get. You can butt up against the cliff edge, which will place you ahead of the trainer since it lets you take the first turn tighter.
Return to the jewel on the sparkling path in Macalania with the Crest, Sigil and Weapon. Present them with the Celestial Mirror, and Caladbolg will attain its true power! Repeat this step for everyone else's Weapon, Crest and Sigil.
Obtain the Nirvana staff from the chest outside the Arena in the Calm Lands. Just use the Celestial Mirror on it and the chest will open.
Grab the Moon Crest from the beach in Besaid. Swim to the right once you hit the water and look for a small cove with a chest in it.
Earn the Moon Sigil by defeating all the Aeons at Remiem Temple. This is pretty simple, provided you got all the Aeons. This includes the "secret" Aeons: Yojimbo, Anima and the Magus Sisters.
Perform the Sending for Belgemine after you have defeated all the Aeons, and you will be rewarded with the Moon Sigil.
Obtain her Godhand by getting the Airship and entering the code "Godhand." This will take you to the lower level of Mushroom Rock. Head to the end of the path and look for the chest.
Obtain the Mercury Crest in the fourth screen of Sanubia Desert, in the northwestern corner.
Attain the Mercury Sigil by completing the Cactuar mini-game. This only can be done after you have the Airship. Head to the Cactuar Glyph outside the sandstorm village and examine it. This will activate the mini-game. You can start now and finish later, but it's easiest to do in one shot.
Find the Cactuars: Tomay - Next to the Oasis, near the Save Sphere. Rovivea - Running around the northwestern corner of the second screen. Chava - Look for the Al Bhed 20 percent sale sign in the fourth area. Examine it. Alek - In the ruins of the third area. Aloja - In the ruins with Alek. Vachella - Hiding in the tent near the Save Sphere in the second area. Robeya - In a chest in the southwestern corner of the third area. Issra - Inside a sand pit in the fourth area. If you haven't already fought the fiend, do that first. You may have to leave, then come back. Elio - At the Oasis, then on the Airship. Head to the outer deck to find him. Flaile - Appears at the Cactuar Glyph after you insert the rest of the Cactuar Spheres.