Why does the Antonov 225 needs 6 crew members?
A quick search points to the following being part of the crew


Pilot
Co-pilot
2x Flight engineers: one on the engine controls; I am not sure of the purpose of the second one but a good guess is hydraulic and electric system monitoring, based on his proximity to the circuit breaker panel (source, scroll down for a 3D photograph of the flight deck).
Navigator: due to the age of the type and the amount of non-standard routes it flies.
Radio operator: same reason as above.


The crew could likely be reduced after a modernization of the cockpit, without upgrading any other hardware like the engines, but the re-certification costs probably outweigh the benefits in this case, for a fleet size of 1.

Mostly sourced from this thread: discussion on Airliners.net about the An-225 crew duties, which also includes good images with annoyingly restrictive copyrights.