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