It just decided not to unlock. I used the bombs on the conveyor belt to blow up the screen, and he said the "fine, let the better man win" (that's not close at all) line. It SHOULD have unlocked, that was my 11th TV. What the carp?
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It's all gotta be done in Chapter 8. I had trouble with a few, you've gotta grab turrets before they stop firing and aim them at the screen.