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