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