Basics
In order to power up the weopons to their powerful self, you will need two items that will power up the ulitimate weopon. When you get the items that relate to the weopon take them to the glowy thing in Macalani Woods to power up your weopon.
Tidus
The Caladbolg
Weopon found at: Race the choccobo women in the Calm Lands and beat her, now go to the upper left of the calm lands. There is a ramp that takes you into the valley, at the marking on the wall examine it and use the mirror, you will then get the weapon.
1st power up item: Sun Crest: After fighting Yunalesca search the battle area where you faught her, go to the far end and go down the stairs, they take you to the front of the room, go back to the stairs and it is in the chest.
2nd power up item: Sun Sigil: Race the choccobo women in the calm lands and get a time of 0:00, to do this get a lot of ballons and little birds.
Yuna
The Nirvana
Weapon found at: Capture all nine enemies in the Calm lands using the weopons you bought from the monster catcher, return to him and he will give you a chest.
1st power up item: Moon Crest: Go to the Besaid beach and get in the water, go to the side away from the docks and you will see the chest (you can get this when you first arrive in Besaid)
2nd power up item: Moon Sigil: After getting all the secret aeons go back to Remiem Temple, fight the aeon women and defeat every one of her aeons, when you do you get to send her, do so to get the item.
Wakka
The World Champion
Weapon found at: Luca Cafe: After winning few blitzball games, go talk to the bartender in Luca, use the mirror and you will have it.
1st power up item: Jupiter Crest: Go to the Aurochs' locker room in Luca, you will find it insider one of the lockers
2nd power up item: Jupiter Sigil: After you get all four of Wakka's overdrive you will get this as a prize for blitzball league games. You must win around 70 games, it starts out fun, but it can get very boring.
Auron
The Masamune
Weapon found at: First go to the area outside of The Cavern of the Stolen Fayth, walk down the path to the right of the save point, you will come across some old pilers, get the Rusty Sword which is stuck in the ground around that area. Now go back to Mushroom Rock Road, remember when you first entered Clasko stopped you from going a certain way, well now you can, go down there and you will come across an elevator thing, take it and you will be at a statue of Lord Mi'ihen, examine it and you will be shown to some markings, use the mirror and you got it.
1st power up weaopn: Mars Crest: Go to the old road in the Mi'ihen highroad, it is in a chest next to a Jecht Sphere.
2nd power up item: Capture every type of monster in at least ten different areas for the monster catcher guy.
Kimahri
The Spirit Lance
Weapon found at: Thunder Plains, go back to the thunder plains, approch any one of the Qactuar Stones, wait for it to glow then press SQUARE. Do this to two more stones, then go to the South path, you will see a Qactuar Ghost flying around, follow him to an old piller, press SQUARE next to the piller and you will get the weapon.
1st power up item: Saturn Crest: After you fight the 3rd Seymore n Gagazent, you will come to some pillers, the chest is in between two of the pillers on the left side.
2nd power up item: Saturn Sigil: Reurn to Macalania Woods and play the butterfly game, capture all the blues and no reds.
LuLu
The Onion Knight
Weapon found at: Baaj Temple: Return to Baaj Temple and defeat Geosgaeno, then search the south part of the pool and you will fing the chest (you can do this on your trip to get Anima)
1st power up item: Venus Crest: Return to the Farplane and get the chest
2nd power up item: Venus Sigil: Avoid 200 lightning bolts in the Thunder Plains consecutively, then return to the Al Bhed Shop.
Rikku
The Godhand
Weapon found at Mushroom Rock Road: Enter the password Godhand on the airship to go to this location, then search the north part of the area.
1st power up item: Mercury Crest: Found in one of the whirlpool sand holes in the desert.
2nd power up item: Mercury Sigil: Complete the Cacture mini-game in the desert.