https://www.twitch.tv/videos/226893308Discovered while playing the brand new free enterprise randomizer (
http://ff4-free-enterprise.com/)
Characters that are hasted and berserked are able to attack monsters that are no longer visible on the screen. This was originally discovered by Crow! against Zeromus, when his hasted characters wound up attacking the upper portion of "Zeromus" (the blue hairball).
I only tested in the common speedrun grind fight to confirm you couldn't get experience by doing it, you can probably do this in a few other battles, such as Magus Sisters or CPU. The behavior itself makes me believe that the game looks at the speed and uncontrolled nature and assume your character is charmed, which opens up targeting invisible creatures.
We have EVEN MORE themes now, but some old ones are gone...