It's an issue with the game. Happens to a lot of people on Regina and Eochaid for some reason. Don't know of any fix offhand.For Regina, walk forward so you're near the point that triggers the cutscene. For Eochaid, fall down from the starting ledge.
If it does happen I just dodge back and to the side as both Eochaid and Regina seem to open up with centered strikes on the party.
Try not to move as the fight begins, as this will trigger this black screen and give the enemy a head start to their attacks.The first part of this is wrong. As said by Atherion and by me, fall down from the initial ledge.
With eochaid, he will start with purely rushing you down (3 hit combo), firing his little causa buddies, or walk towards you, which the first was the one that ended up incapacitating you.