Here is the full list of all 28 FINAL FANTASY II achievements. It takes around 15-20 hours to unlock all of the achievements on Windows.
Became allies with Ricard the dragoon.
Collected treasure from 50% of the chests.
Defeated Commander Gottos and reclaimed Castle Fynn.
Completed 50% of the Bestiary entries.
Obtained a ship from the pirate Leila.
Blew up the Dreadnought.
Obtained 100,000 gil.
Obtained 50,000 gil.
Collected treasure from 10% of the chests.
The empire destroyed numerous towns with the Dreadnought.
Defeated 500 monsters.
Obtained 10,000 gil.
Completed 10% of the Bestiary entries.
Defeated 300 monsters.
The rebellion commenced against the Palamecian Empire.
Defeated 100 monsters.
Earned all achievements.
Hatched the last wyvern egg.
The Dark Knight ascended the emperor's throne.
Past allies joined the rebel army.
Defeated the emperor and restored peace to the world.
Obtained Excalibur.
Learned all passwords.
Leveled up one weapon type to skill level 16.
Leveled up one magic spell to skill level 16.
Completed 100% of the Bestiary entries.
Collected treasure from 100% of the chests.
Traveled to all the map locations.