There are a few things you have to do in order to get your hand on Ultimate Weapon.

To get the Ultimate Weapon, you have to fix princess Sara's pendent first. However, you to unlock this quest, you have to talk to MogNet as Ingus to get a mail from the princess first. After you did, go to Castle Sasune, east tower, and talk to princess Sara.

Now bring the pendent to Kazus and talk to Takka. He will reject your request simply because he cannot fix and said only the Legendary Smith can do it. It's time to find her, she is in Northwestern Saronia.

After the pendent is fixed, bring it back to princess Sara. 

Next, you need to find Orichalcum for the Legendary Smith so that she can make the Ultimate Weapon. Go back to The Invincible and talk to MogNet as Luneth.This time, you should see a new mail from Cid telling you that there is something in his basement.

Head back to Canaan, Floating Continent. Inside Cid's house, talk to him and he will tell you that there is a monster inside his basement. The monster is actually the Orichalcum so kill it and it back to the smith. 

Unfortunately, the Legendary Smith is not in Saronia anymore but in Falgarbard.

After watching a show, she will give Ultima Weapon.

Master Cards and Mastery Items are given by Legendary Smith after reaching job level 99. Each job has its unique item and can only be obtained one from the smith. Only the job itself can use its own item.

Once you reach job level 99, you need to find the Legendary Smith; her location is random though, then talk to her while using the job. Below is her locations where she appears randomly:

• Ur: Inside the well.
• Castle Sasune: The East Tower's third floor
• Healing Copse
• Village of the Ancients: inside The Inn.
• Gysahl: Inside the Chocobo stable.
• Dwarven Hollows: The entrance to the Subterranean Lake.
• Replito: At northern house, there is a hidden door behind the house.
• Saronia Castle: The hidden passageway in the left area where the two Black Mages are.
• Doga's Village: in the middle island.
• Ancient Ruins: inside The Inn.

Finding in these random locations is a pain in the ass. Here is a much easier strategy: since her appearance is random, you can always in/out between 2 of the above places. Luckily, Healing Copse and Gysahl are the closest to each other, all you need to do is fly between these locations while in Mini state.