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