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 Iron Giant.
Attain level 99 with all jobs for all characters.
Complete the entire Bestiary.
Obtain the Ultima Weapon from the Legendary Smith.
Defeat the Cloud of Darkness.
Save up 500,000 gil.
Obtain every weapon in Eureka, the Forbidden Land.
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.
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.