Right
before the mini-boss of level 4, you'll run into Cecile. She'll start
to attack you, so break out the Invincibility assist really quickly or
you'll take quite a few hits. Run up to her and use your Crystal attack
to freeze her, then jump on her head and make your way up the ladder...
This
is as far as you can go, don't even bother attempting to jump into the
area with the brain-like mini-boss. Ok, in order to defeat it, you'll
have to shoot it about 3 or 4 times with each ESP attack you've got. They
have to be done in a specific order, or else they have no effect. Just
keep using your Invincibility assist(doesn't matter if you use up all
of your ESP meter, you don't need it after this), then scroll through
each attack, jump up and shoot. If the brain blinks white, you hit him.
Move on to the next attack, and try it...if it doesn't blink, move to
the next...so on and so forth.
After
beating the brain, Dr. Knavik will reveal himself and challenge you to
a duel. This is where things get kinda weird. You can't really attack
here, you can only hit Up or Down to fly. If he goes down, press Down
to fly by him(I assume she hits him each time she flies by him), if he
goes up, press Up. I don't know that you can actually loose this duel,
so don't worry about messing up. After about 4 or 5 passes, he'll drop
back down to the ground...