Tidus' ultimate weapon is called the Caladbolg. You get it after you race with that chocobo dude, then the guy at the far corner of the calm lands moves out of the way, so you can get the weapon from the treasure chest.

As for the crest and the sigil, you can get one of them from the area where you fought Yunalesca revisited, and you can get the Sun sigil by getting a 0.00 time in the chocobo race thingy by not getting hit by birds, and collecting a lot of balloons. (I found it to be very frustrating)

But, you can only upgrade the weapons with the crest and the sigil after you get the celestial mirror. First, go to the area where you can challenge Belgemine, and in the outer area, if you race correctly with the chocobo. Then you oibtain the cloudy mirror., After that, you do some Macalania woods sidequest to get the celestial mirror. To upgrade weapons, take the weapon with the crest and/or Sigil to the plant where you got the celestial mirror, and then upgrade it.

Remember, the weapon is useless without the crest and sigil.(Although it's effect which raises your attack when your HP is high still works)