The 2001 adaptation arguably has the best fight scenes of all the Cyborg 009 media.
Seriously, from the getgo in episode one, you KNOW it's going to be an awesome series from the FIGHTS ALONE!
The "Attack of the Gods" arc with the fake Greek gods was totally awesome.
009 vs 0010 and 0010!
When 004 battles a robot replica of himself, they fight so intensely that the difference can't be seen between the two — but when the robot knocks down an innocent bird's nest in one of its attempts on 004's life, 004 catches the nest and shields both mother bird and babies with his own body, proving that he is a human and not a machine. Also a Crowning Moment of Heartwarming (the manga equivalent is a little more bittersweet).
003 gets hers when she almost singlehandedly hijacks a plane to stop some mafia groups from releasing a deadly virus in Cairo. Defeating several guards without spilling a single drop of blood and disarming the bomb on her own, without any guidance from Gilmore? A-we-so-me.
004's battle with the robot replica is a bit darker in the original manga story "The Bizarre Machine", with the fake 004 brutally crushing the nest of baby birds beneath his foot, then murdering their mother. But in the end, the real 004 manages to get the upper hand over his replica due to that distraction, and shoots it full of bullets, remarking that his lingering humanity and "weakness" is what proved him to be stronger than the robot.