The reason that most people stop shooting during borders in boss fights is because you only get a border for every 50,000 cherry you accumulate, and most boss attacks give a massive amount of cherry when you clear them since you get points for any remaining bullets.
A good example of this is Ran. Even if you go into the fight with 0/50,000 cherry, the end of her first non-card will likely throw you straight into the 50,000 threshold and activate a border. Clearing Wizard Fox Thoughts (her first card) will give you about 39,000 cherry, so you'll be almost towards a second border. A third border is then given outright by her second non-card because there are that many bullets, then much more cherry is given at the end of her second card.
By the end of Charming Siege From All Sides (Ran's fourth card), you could potentially have seen no less than seven Borders, each worth anything from four to five million points if they don't get burst, 28-35 million in total.
But this can go wrong. Say you get the border during Fox Laser and stay under Ran, grazing the laser all the while for massive Maxcherry bonuses. If you forget to stop shooting Ran while you're doing this and you end the card, you'll get the bonus cherry whilst a border is still up, meaning the bonus is wasted.
As for Phantasm: the stage is frantic but doable and once you've passed Yukari's first two cards, it's almost like a rematch with Ran until her eighth card. I beat her on my fifth attempt.