I've gone through the Wonderswan Color version in under 4 hours, but there isn't a really good way to record a Wonderswan Color game. The time of 4:55 I've been told is not that fast, but I don't really know what a "good" time is for Normal Mode on the PS1 version. The most efficient party is probably 3 Warriors and a Red Mage, but I use the Thief for the above reasons. I go with this party in the Wonderswan Color version (which I can beat an hour faster than this one) and this one mainly in hopes that the Thief can run away decently, and as a Ninja for a couple of spells that character can cast (namely sutorai and Haste). The party I chose is Warrior, Warrior, Red Mage, Thief.
Part 2 is a 'single segment', all the way through.
Part 2 is my first try at the second half, and since I completed it, I took it. Part 1 is really 3 parts I died a time or two at the Castle of Ordeals and also died a time or two at the Ice Cave. The video is separated into two parts, but they are not two 'single segments'. The game is played on Normal Mode, not Easy Mode. The version played is the Japanese version, mainly because it is the one I am used to (control-wise) and that this version does not have that "dancing cursor" problem (where the cursor seems to move on its own while the player is choosing an option, resulting in going to an undesired command) that the US version has in the game.
This is my ~4:55 video playthrough of Final Fantasy 1 on the PS1. Speed run of Final Fantasy 1 (PS1) in ~4:55.