I attempted a legitimate speed run of FF4 some time ago - got to the Tower of Zot in 1:30 before quitting due to lack of time.
The walkthrough on GameFAQs was a bit vague, and there's lots of ways to improve his 8 hour run, most notably cutting down on the amount that you need to level up. I've found that there's really only four locations that are absolutely necessary to level up in:
- Cave north of Kaipo, right after you get Rydia. Beat up on the monsters weak to Lit (use Tellah to wipe them out in one shot) until you get high enough level to get Lit-1. This should give Rydia more durability in the fights to come, as well as give her more MP to summon her Chocobo. You should be able to do this while walking normally before you get to the save point halfway through the cave.
- Fight a couple battles just after changing Cecil into a Paladin, since you can gain so many levels with him in such a short amount of time, that it's a pretty good idea you do so.
- Harvest summoned enemies off an Alert (a monster-in-a-box in several chests) in the Tower of Bab-il in the underworld. To do this, smack the Alert with a weak attack (preferably Rydia's or Rosa's), and the Alert will summon a monster. Kill the monster, and smack the Alert again. Rinse and repeat until you're high enough level to take on most of the rest of the game. You'll get EXP off each monster you kill, and it's much better than walking around fighting random battles.
- Harvest Attackers/Defenders while fighting the CPU boss in the Giant of Babil. This is by far the quickest way to level in the entire game. Attackers just fire off Maser (which eats off 1/8 of your max HP to all party members), and Defenders only heal the CPU. You'll want to buy lots of Life1s prior to coming here, though, since if both the Attacker and Defender are killed, it'll use Globe199 twice, which instantly kills two party members, before resummoning another Attacker and Defender. You should be able to level to 60 or so in 15 minutes to a half an hour, especially since we're tool assisting the battle, which should be high enough to beat the rest of the game.
I expected a run of five hours at the game, and if you tool assist the menus and the battles, and plan which chests to get carefully, you can probably smash that time fairly easily, maybe even go under four and a half hours.