if even one is active, you'll fail and have to backtrack and deactivate it
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Or jump around the barrier.
I've only ever successfully jump around one barrier. I am sure skilled players could jump around them all. And I believe the Dark path is faster... but I'm not sure. Dark path is easier to get Chaos Control on, that's for sure.
If you prefer the route for the Black Hawk, which I used twice to get my high score for the hero mission of this level, shoot the switch, go behind the door that the switch would have otherwise blocked, and shoot the switch again. You can now use the Black Hawk ride without it stopping you from getting to Black Doom.
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It's so obvious. XD I dunno why I didn't think of this. Still, that makes it a toss up between which you are better at or can do faster: marksmanship, or (spindash) jumping.