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

1. Open the door to Eureka.
2. Fix princess Sara pendant.
3. Complete "Something in the basement..." quest from Cid. This will give you Orichalcum, the material you need to acquire the Ultima Weapon.
4. Getting Ultima Weapon from the Legendary Smith.

To get the Ultimate Weapon, you have to fix princess Sara's pendant first. To unlock this quest, you have to talk to the MogNet on the left on The Invincible as Ingus. Read all letters from princess Sara (the last one has the title "Help.."). After you did, go to Castle Sasune, east tower, and talk to the princess.

Now bring the pendant 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 pendant is fixed, bring it back to princess Sara. 

Next, you need to find Orichalcum for the Legendary Smith so that she can make the Ultima Weapon. 

Go back to The Invincible and talk to the 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 will drop Orichalcum after you killed it. 

IMPORTANT: Before you leave the house, talk to Cid one more time so that he confirm the Unknown Metal is actually Orichalcum.

This time, the Legendary Smith is not in Saronia anymore, she has traveled to Falgarbard.

After watching the dialogue, she will forge Ultima Weapon for you.