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