Northwest corner of the Calm Lands, behind a mandala at the bottom of a very narrow hidden trail. Win all four chocobo races, and the person blocking the pathway will be gone. You must  have the Celestial Mirror in your inventory to get the weapon, otherwise the guard will not move.

Yevon Dome, in a treasure chest in the same area where you fought Yunalesca. You may have to go up and down the stairs once or twice to get the chest to appear. It's on the left side of the screen, and blends in with the wall.

After you can control the airship, it's a prize for winning the fourth chocobo race against the other chocobo rider with a time of better than 0:0:0. TIP: Use the D-pad for this race. Grab balloons! It's the only way to win the sigil.

In a chest at the Monster Arena to the east of the Calm Lands, after collecting at least one of each monster from the Calm Lands. Although you can find the chest before leaving the Calm Lands, you MUST have the Celestial Mirror in your inventory to open it.

Besaid Island beach, in a chest in a cove on the east side, only accessable by swimming. You can get this very early in the game.

Defeat all of your Aeons at Remiem Temple, then preform the Farplane Sendoff for Belgemine. All of your Aeons means ALL of them, including the secret ones like Youjimbo, Anima, and the Magus Sisters.

Behind a mandala at Mushroom Rock Road. At the bottom of the Calm Lands valley, at the opposite end of the crevasse from the Cave of the Stolen Fayth, take the Rusty Sword from the rocky alcove. Then go to Mushroom Rock Road and continue straight ahead north until you see a little green square on the area map.  It's the second left on the first screen of Mushroom Rock Road. The green square represents a floating mushroom stone, ride it up to a plateau, and stick the sword in the ground next to the statue of a warrior standing over a slain behemoth. The mandala will appear on the wall behind you. You MUST have the Celestial Mirror in your inventory to get the weapon.

In a chest in the old part of Mi'ihen Highroad. To get there, go north on Mi'ihen Highroad until you reach the entrance of Mushroom Rock Road, then hang a U-turn and go south.

Unlock any combination of 10 Area Creations or Species Creations bosses at the Monster Arena to the east of the Calm Lands, and the trainer will give this to you. Area Creations are unlocked by capturing at least one of each monster in a particular area, and Species Creations are unlocked by capturing several of each monster from a particular species - Bombs, Wolves, or Floating Eyeballs, for example.  And if the trainer doesn't give the Mars Sigil to you, either a) keep chatting with him until he does, or b) you didn't unlock enough special bosses - Original Creations do NOT count towards your total.

In a sealed chest at the bottom of Mushroom Rock Road, accessable by selecting Password on the airship, then inputting "GODHAND". You MUST have the Celestial Mirror in your inventory to get the weapon.

In a treasure chest in the fourth area of Sanubia Desert (the screen just before Home), in an alcove to the northwest. If your area map is turned on, you cannot miss this.

Sanubia Desert, in a treasure chest in the area protected by a sandstorm. To get rid of the sandstorm, you need to play a hide-and-seek minigame with the Cactuars after you can control the airship. (You can examine the Cactuar glyph during your first visit to Sanubia Desert, but again, you cannot play the minigame until you have the airship.) Check my extras for more information about the hide-and-seek game.

In a sealed chest in the pool at Baaj Temple, hidden in a corner on the opposite side of the pool from the doorway to Anima's shrine. The chest will not appear until you've defeated Geosgaeno, and isn't visible until you're literally right on top of it, so dive deep and keep hitting the [X] button to search for the chest. You MUST have the Celestial Mirror in your inventory to open the chest. And believe me, you won't know you've found the chest until the game asks if you want to use the mirror.

In a treasure chest that appears during your second visit to the Farplane. You can get this after you've finished everything you need to do in Guadosalam for story purposes.

Dodge the lightning at Thunder Plains 200 CONSECUTIVE times by pressing [X], then go back to Rin's travel agency and examine the treasure chest out front. Do not save in between dodges or leave the screen, because this will reset the dodge counter. Also, don't just sit there and hammer [X], or use a turbo controller, because the game senses you're trying to cheat, and will zap you with lightning just to annoy you. You can get the Sigil on your first visit to Thunder Plains, long before obtaining the airship, unlike everyone else's Sigils.

At Thunder Plains, pray by pressing [square] at any 3 glowing Qactuar stones, then return to the south part of the plain and follow the Qactuar ghost to a wrecked tower. It's on the right side of the screen, embedded in the rock wall, equidistant from the north and south boundries of the plain. Pray there. Although you can find the chest during your first visit to Thunder Plains, you cannot open it until you have the Celestial Mirror. NOTE: In the Japanese FFX, Kimahri's ultimate weapon was called Longinus, which is the name of the Roman soldier who pierced Christ's side with his spear. The metaphor of a spear that could pierce the divine is lost in the English translation.

Mt. Gagazet, in a treasure chest between the pillars on the left, just past where you fought Seymour. If you can't find it, you don't deserve to be playing this game.

Macalania Woods butterfly-catching game, _after_ getting the airship. There are technically 3 different versions of this minigame, each at a different difficulty with different prizes: (1) upon first entering Macalania Woods, (2) after fighting the Spherimorph, and (3) after you can control the airship. To start the minigame, talk to the harp- playing demihuman near the entrance, then touch the blue butterfly. The object of the game is to touch all the blue butterflies in one area before time runs out. If you touch a red butterfly, you'll automatically have to fight a battle, and lose a few seconds.

After you can control the airship, the bartender in Luca Cafe will give this to you if you've won at least 5 Blitzball games. You MUST have the Celestial Mirror in your inventory to get the weapon.

Luca Stadium, in a locker in the Besaid Aurochs locker room. You can get this after you've finished everything you need to do in Luca for story purposes.

After winning all four of Wakka's Overdrives, this is a random grand prize in the Blitzball League game. Could take 50 games if you are lucky, or closer to 500 if you are not. Believe it, I'm not very lucky myself. Fortunately, I love playing blitzball.