There are positive proofs for helmets painted red and black. Blue is much more questionable, as this colour is often used to show polished iron or silver. I do believe in blue painting, but you will find many who will argue against it.

Red and black are supported by helmets painted on the walls of macedonian Lyson&Kallikes's tomb and by common usage of such helmets in medieval period.
Blue appeares on many objects, for example on so called "Alexander's sarcophagus" from Sidon.