Here is the full list of all 18 Final Fantasy III (3D Remake) achievements. It takes around 200 hours to unlock all of the achievements on Windows.
Attain level 99 with all jobs for all characters.
Complete the entire Bestiary.
Defeat Iron Giant.
Open every treasure chest.
Defeat the Cloud of Darkness.
Attain level 99 with any job.
Obtain every weapon in Eureka, the Forbidden Land.
Obtain the Ultima Weapon from the Legendary Smith.
Save up 500,000 gil.
Obtain all the summonable creatures.
Defeat Titan and obtain the Earth Crystal.
Complete 50% of the Bestiary.
Open 50% of all treasure chests.
Obtain a summonable creature.
Save up 50,000 gil.
Defeat Kraken and obtain the Water Crystal.
Defeat Salamander and obtain the Fire Crystal.
Defeat Djinn and obtain the Wind Crystal.