The Celestial Weapons are the strongest weapons available for each of the characters available in the game. In order to fully unlock the weapon you must also obtain the corresponding crests and sigils in order to add on abilities. The weapons start off with the "No AP" ability only which makes them start off as entirely useless.
In order to use the corresponding crest and sigil on a Celestial Weapon you will need to obtain the Celestial Mirror. Click on the link below for more information:
Once you have obtained the Celestial Mirror you can begin obtaining and powering up each Celestial Weapon. Click on the Celestial Weapons below for more information on how to obtain them:
The Celestial Weapon for Tidus obtained in the Calm Lands.
The Celestial Weapon for Yuna obtained by capturing monsters for the Monster Arena.
The Celestial Weapon for Auron obtained after you locate the statue of Lord Mi’ihen.
The Celestial Weapon for Wakka obtained by completing and winning a Blitzball tournament.
The Celestial Weapon for Lulu obtained by completing Baaj Temple.
The Celestial Weapon for Kimahri obtained in the Thunder Plains.
The Celestial Weapon for Rikku obtained by entering an Al Bhed password whilst on the Airship.