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.
Open every treasure chest.
Attain level 99 with all jobs for all characters.
Complete the entire Bestiary.
Obtain all the summonable creatures.
Obtain the Ultima Weapon from the Legendary Smith.
Obtain every weapon in Eureka, the Forbidden Land.
Save up 500,000 gil.
Defeat Titan and obtain the Earth Crystal.
Obtain a summonable creature.
Complete 50% of the Bestiary.
Attain level 99 with any job.
Open 50% of all treasure chests.
Defeat Kraken and obtain the Water Crystal.
Save up 50,000 gil.
Defeat Salamander and obtain the Fire Crystal.
Defeat Djinn and obtain the Wind Crystal.