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.
Defeat Iron Giant.
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.
Defeat Titan and obtain the Earth Crystal.
Save up 500,000 gil.
Obtain all the summonable creatures.
Defeat Salamander and obtain the Fire Crystal.
Defeat Kraken and obtain the Water Crystal.
Save up 50,000 gil.
Obtain a summonable creature.
Open 50% of all treasure chests.
Complete 50% of the Bestiary.
Defeat Djinn and obtain the Wind Crystal.
Open every treasure chest.
Complete the entire Bestiary.
Attain level 99 with all jobs for all characters.