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.
Complete the entire Bestiary.
Defeat Iron Giant.
Defeat the Cloud of Darkness.
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.
Complete 50% of the Bestiary.
Obtain a summonable creature.
Open 50% of all treasure chests.
Defeat Kraken and obtain the Water Crystal.
Defeat Salamander and obtain the Fire Crystal.
Attain level 99 with any job.
Defeat Djinn and obtain the Wind Crystal.
Save up 50,000 gil.
Save up 500,000 gil.