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