This is a pesky issue. I understand that although it doesn't affect all PS4 users, ( which is weird) it affects a lot. I sympathize, especially as I stare at my Arkham Knight game on PC.
Thanks for your feedback, it's good to know that you guys acnowledge this issue, and even know that it's as bad as the Batman game on PC.
Can you say why the game literally LOCKS the framerate at 20 sometimes? It's makes the fights much harder, and cinematics very choppy.