Is the game maybe on a hard drive, not an SSD? Because this one animation is something special and I don't think it's preloaded. I probably don't notice it because my hard drive is a bit faster than a normal HDD or SSD. But I will see what can be done to load this animation at the beginning of the fight when Alina is involved in the fight. Then the delay should no longer be present on slower systems or slower storage media.
Since you can change the difficulty at any time and the points are not calculated per round but at the end of a week, this would only be exploited. Play the first three fights on easy and then defeat the boss on hard to get more points for example. As I said, the level of difficulty is only there to challenge yourself.