In this video I complete Final Fantasy IV in less than 22 hours, which was just a leisurely stroll through the game. Even though this is not a record, I was still able to get Rydia's side quest summons (even though I did not spend the time to get the ones which are obtainable from random battle drops). I got all the armor from the lunar basements and core, but I did not feel like wasting time to get the pink tail rare drop for the adamant armor. Basically I just cruised through the game to arrive at the ending, gathering the main things along the way.
I complete the quest to the moon's core from the last possible save point. This includes the final battle with Zeromus and the ending of the game. This was completed on the playstation Final Fantasy Chronicles Version of the game. You will notice the added video segments during the ending of the game after the coronation ceremony and before the final credits.
You will notice that the final battle was troublesome to a certain degree because a single big bang could take out Rydia. After a couple rounds I just learned to leave her dead rather than waste resources.