How do you defeat Emily Jefferson without running out of people to possess?

After fighting this boss for a while, it releases some red missiles, which you don't seem to be able to dodge and they kill you instantly. I can overdive into someone else when attacked by them, but I always run out of people to dive into, so this is not really an option imho. So how do you actually defeat this boss without running out of people to dive into?

You can dodge that attack from three different manners:

• Dive into someone else, and sacrifice the one you were controlling.
• Enter the fury mode, that attack is automatically cancelled in this mode.
• Trick the projectile in a wall, but that is fairly difficult.

Also, if your mens dies too quickly, you may just not have a level sufficient to attempt the boss, TTB is supposed to be played from Easy mode the first time, then normal, then Hard...