This Seeking Tech guide will show you how to to Living Woods, which is the only permanently missable location in the Pixel Remaster version of Final Fantasy III.
If you don’t unlock this location before it disappears completely, then you won’t be able to earn the Adventurous Wayfarer trophy and achievement.
The Living Woods is located on the western side of the Floating Continent, as you can find it directly southwest of the big waterfall.
The earliest point in the story that you can gain access to this location is when you get the ship and complete the Nepto Temple. You should then be able to sail there directly.
If you haven’t visited Living Woods before beating the Castle Hein dungeon, then it will be locked out for the rest of the playthrough.