On a 2010 training exercise, a team of Navy SEALs converged on an ocean rendezvous point. Crouched beside the sailors on a bouncing Zodiac speedboat was a filmmaker, dressed in camouflage with his camera rolling as a submarine broke the surface. "We ran those boats right up on the back of that nuclear sub," said director Mike McCoy.

His team came to film the SEALs perform an underwater exit from the sub, then spent a week alongside its crew when rough seas dragged out the two-day shoot. For two years the filmmakers had inside...