Well the Kaiju is actually constantly moving so it's never in the same place, and I was kinda iffy on adding attacks since I thought they looked corny at the time. As for how I did the fog, Unreal utilizes Post Process and I simply applied it to the character. You could even set the distance between the player and the fog, and from experimentation, I learned that by applying a zoom, the fog will move with the camera, making it look like you can see beyond the fog when you're recording.
Had to mess with the settings a little but the end product turned out great.