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