Final Fantasy III Checklist

Getting Onion Knight

Unlock 25% of the bestiary.

If you find and defeat all new enemies as soon as they become available, you will reach this point when you finish Tower of Owen. You can check your bestiary in Gysahl.
Read all four MogNet letters from Topapa (with Luneth).
Return to Ur and talk to Topapa.
Go to Altar Cave and complete the quest.

Legendary Smith

Legendary Smith is the source of Ultima Weapon and job-specific ultimate weapons for jobs that reach job level 99.

After Cave of Tides:

Check MogNet with Ingus and read all four letters from Princess Sara.
Return to the Floating Continent, talk to Princess Sara in Castle Sasune and then Takka in Kazus.
After Saronia:

Check MogNet with Luneth or Arc and read all four letters from Takka.
Talk to the smith in Northwester Saronia.
After acquiring Invincible:

Check MogNet with Refia and read the fifth letter from from Takka, followed by all four letters from Cid.
Go to Canaan, complete Cid's quest and talk to him.
After unlocking Eureka:

Talk to the smith in Falgabard.

After that, the smith is "unlocked". She will continue to appear randomly in one of several places (see the relevant wiki section for details) and if you talk to her whenever you reach job level 99 in a job, she will give you that job's card (key item) and ultimate piece of eqipment (once per job).

Unlock ???

Complete the requirements:
- Unlock 80% of bestiary.
- Unlock the Legendary Smith.
- Defeat every boss in Eureka.
- Reach job level 99 with any job and get the job card from Legendary Smith.
Read all four letters from The 4 Old Men and Prince Alus (with Arc).
Use Nautilus to find and enter the dungeon.

??? is located directly west of the very tip of the Dalg continent (where Doga's Manor is). Look for a shadow in the water, dive underwater next to it and enter the middle of the corals.