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