One thing you can do, assuming you have access to multiple classes, is to try the fight with a class that's less demanding. Rather than trying to learn the fight and learn your rotations at the same time, you might be able to learn the fight first as a class like a ranged DPS. Then it will be easier for you to slot your melee DPS skills into the fight once you already have a better idea of what to expect.

While I don't do the hardcore content in the game, I often find myself first running fights as a Red Mage or even Dancer to get used to them and then moving to my Samurai once I'm more comfortable with the fight as a whole.