Four dungeons? Two you mean. Sylx Tower and Dark World are the only two dungeons with no savepoints in between. Eureka you can save outside Sylx Tower and Ancient's Maze just as well.

And there are healing springs in Eureka. And it's really not that hard to go back through ancient's maze to the Invincible...

Besides that, yup, I beat FF III NES. Two times even. The second time I beat it with an end party that had no Ninjas or Sages, but a Knight, Mystic Knight, Shaman and Summoner. Hard, but beatable. I was lv 52 the first time I beat it. I was lv 60 the second time I did it. I will probably play it again sometime, but for playthroughs through III NES, there needs to be some time in between.

Loved the Final Dungeons. Dark World especially was awesome, but hard. Those four bosses are killer. And the Final Boss is a matter of luck and skill, especially when you're not using Ninja's and Sages. But I still love this game. Best FF ever.