A research team managed to film an adult Architeuthis in its natural environment, 900 meters below sea level. They used a shrimp lure to draw it in. Unfortunately, it was snagged and lost a tentacle before escaping. Based on its escape attempts, the squid appears to be rather more energetic than had been previously assumed.
The BBC story, which has links to video.
The article also discusses how the fishing practice of bottom trawling may be destroying squid egg beds on the sea floor. Their evidence for this is indirect -- sperm whales swimming through areas that were traditionally rich in giant squid are no longer able to find squid to eat.