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 Salamander and obtain the Fire Crystal.
Defeat Djinn and obtain the Wind Crystal.
Defeat Kraken and obtain the Water Crystal.
Defeat Titan and obtain the Earth Crystal.
Defeat the Cloud of Darkness.
Obtain every weapon in Eureka, the Forbidden Land.
Save up 50,000 gil.
Save up 500,000 gil.
Obtain a summonable creature.
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.