Celestial Weapons
Tidus - Caladbolg
Abilities - Break 9999 Damage, 3x Overdrive, Avoid Counter, Magic Counter
Weapon - Found in the northwest end of the Calm Lands, down a narrow pathway. A person blocks the way until you win all four chocobo contests in the Calm Lands. The chocobo trainer is in the center of the area, near the save sphere.
Crest - Return to the room in Yevon Dome in which you fought Yunalesca. The crest is in a treasure chest.
Sigil - Re-do the fourth-chocobo training race in the Calm Lands and achieve a time of 0:00. Just try to avoid the birds as much as possible and try getting as many balloons as you can. You probably won't do this in the first few attempts, but the balloon arrangement is random, so the odds might be in your favor eventually.
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Wakka - World Champion
Abilities - Break 9999 Damage, 3x Overdrive, Double AP, Avoid Counter
Aeon Effect - Grants Ifrit to be able to break the 9999 damage limit.
Weapon - The World Champion ball is given to you from the Luca bartender once you've won 5 Blitzball games.
Crest - Located in the Besaid Aurochs' locker room at the Luca Stadium.
Sigil - Found as a grand prize in Blitzball. Must first have all 4 of Wakka's overdrives.
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Yuna - Nirvana
Abilities - Break 9999 Damage, 3x Overdrive, Double AP, MP Cost 1
Aeon Effect - Valefore is able to break the 9999 damage limit.
Weapon - The monster trainer in the Calm Lands gives the weapon to you once you get 1 of every creature found in the Calm Lands.
Crest - Go back to the Besaid Beach. Yuna's Crest is in a chest there. Swim into the water and go up to the coastline until you see it.
Sigil - You get her Sigil after beating all eight of the Bergimene's Aeons in the Remiem Temple. In order to get to the Remiem Temple, you must first go into the Calm Lands and get a Chocobo from the Trainer. Then go back to the entrance of the Calm Lands. Once there, head to the far right, and you'll find a feather which signals the Chocobo to jump. From there, you can find your way into the temple.
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Auron - Masamune
Abilities - Break 9999 Damage, 3x Overdrive, Pre-emptive Attack, Counter
Aeon Effect - Allows Yojimbo to break 9999 damage limit.
Weapon - Located near the cave under the Valley (located underneath the bridge at the end of the Calm Lands) you'll find a Rusty Sword. Take this sword to the Mushroom Rock Road. On the left side of the road, you'll notice a small nook with an elevator. Insert the Rusty Sword into the battle statue there to receive the Masamune.
Crest - Found in a chest on the Old Mi'ihen Road. (Requires a Chocobo to reach)
Sigil - Requires you to capture one of each monster in 10 different monster catching areas. The monster trainer will reward you with Aurons Sigil.
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Lulu - Onion Knight
Abilities - Break 9999 Damage, 3x Overdrive, Magic Booster, MP Cost 1
Aeon Effect - Shiva can break the 9999 damage limit.
Weapon - To find this weapon, return to the Baaj Temple. You'll find a chest near a wall in the lake. When the camera starts zooming in, you're close.
Crest - Go back into the Farplane in Guadosalam to find the Crest.
Sigil - Return to the Thunder Plains to begin the quest. If you can dodge 200 consecutive bolts of lightning by pressing the X button when the screen flashes successfully, you'll be rewarded by finding a chest in front of the Inn which contains the Sigil. This little mini-game will take about a half hour.
WARNING - Trying this is a completely insane. Don't attempt doing this unless you're one of those people who simply has to get everything.
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Rikku - Godhand
Abilities - Break 9999 Damage, 3x Overdrive, Double AP, Gillionaire
Weapon - While on the airship input the password GOD-HAND and in the location, grab the actual weapon from a chest located not far off from where you land.
Crest
Take it from a chest in the northwest corner of the Sanubia Desert (fourth area)
Sigil
Play a Cactuar mini-game in the Sanubia Desert to find the Sigil. Start at the Cactuar monument in front of the sand storm. This tells you about the 10 Cactuars. When you find each of them, each will play a game with you. In this game, you must catch them before the time runs out, and they can't be onto you. You don't really need to win these little games, you'll still get an orb even if you fail. You must return all the orbs individually to the monument in order to get the Sigil below. When you complete one Cactuars mini-quest, you'll be prompted to do another by the monument, the monument gives you little clues. But each of the mini-quests come at random and have no specific order, so here are all of them.
1. Tomay - At the Bikanel Island oasis (1st desert area)
2. Rovivea - Northwest area of the 2nd desert area
3. Chava - Hiding behind the Al Bhed 20% off sign in the 4th area
4. Alek - Running around the ruins in the West section of the 3rd area
5. Aloja - Same as above
6. Vachella - Hidden behind the save sphere in the 2nd area
7. Robeya - In a treasure chest in the Southwestern part of the 3rd area
8. Issra - In an antlion pit in the 4th area. (But you must first leave the 4th area and return for the Cactuar to be there)
9. Elio - At the Bikanel Island oasis, but he warps onto your airship. He can be found inside the airship.
10. Flaile - He appears back at the monument once you get 9 Cactuars
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Kimahri - Spirit Lance
Abilities - Break 9999 Damage, 3x Overdrive, Double AP, Avoid Counter
Aeon Effect - Ixion breaks the 9999 damage limit.
Weapon - You'll find some glowing Cactuar monuments located throughout the Thunder Plains. Press the Square button to pray at three of them. Then, follow the ghostly Cactuar that appears to a wrecked thunder tower. Pray at the base of the tower to uncover a treasure chest, which contains the weapon.
Crest - Go back to Mt. Gagazet, just a little beyond where you fought Seymour. It's located behind a pillar on the left.
Sigil - Win the butterfly-catching mini-game in the Macalania Forest. What you do in the mini-game is touch all the blue butterflies within the allotted time limit. Touching a red butterfly engages a battle and wastes some time. This is harder than it seems. Believe me.
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Secret Aeons
Anima
Seymour's Aeon can be yours, I assume you've already collected the Destruction Sphere treasures from the 6 Aeon shrines already. If you missed a few, you can return to the shrines after beating the Seymour inside Sin. Input the airship co-ordinates X16 Y57 to reach the Baaj Temple. Tidus, Wakka and Rikku jump into the lake and Tidus vows to finish something he started with an aquatic beast that bested him in the start. This beast can prove to be difficult. Rikku's grenades and gems will make the battle a lot easier. Once you get that thing out of the way, you'll dive into an undersea Fayth. Yuna will pray here and receive Anima.
Yojimbo
You'll find Yojimbo in the forgotten cave between the Calm Lands and Mt. Gagazet. You can find the cave underneath the bridge at the exit of the Calm Lands. You'll encounter a spirit in the cave. She'll summon Yojimbo to fight you, but he's a complete pushover to beat. Afterward, Yuna will be able to enter the Fayth. However Yojimbo will not join the party for free. He requests 300,000 gil for his services. Although you can probably haggle the price down to around 170,000-200,000. He has no real overdrive, and can't cast spells, and won't let you control him. He asks for money for each attack. You can pay 1 gil for his normal attacks, or fi you pay him lots of gil he'll whip out Zanmato, an Odin-ish move which slices enemies in half.
Magus Sisters (Cindy, Sandy and Mindy)
First, you must capture 1 of each monster in the Calm Lands and Mt. Gagazet. Return to the monster trainer in the Calm Lands to receive a small prize. Once you get all 21 creatures, go to the southeast corner of the Calm Lands on a chocobo. You'll see a feather on a ledge. Use it to get your chocobo to jump to a hidden ledge. Then, get off the chocobo and get to the Remiem Temple. Yuna must now face off against an Aeon trainer against every Aeon she has. You can heal between fights, so it shouldn't be too hard. Eventually, you win two items that will open the nearby door to the Fayth of the Magus Sisters. On the way out, you can challenge the Aeon trainer one last time for a special item. She uses the Sisters in the last fight, so use Anima for the last duel.
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*places hands in a large bowl filled with cold water and ice* Ahhhh, that's refreshing. Anyways, I hope this helped.
Edit: *fixes some typos*