I've actually beaten an insane enemy....very hard stuff though. But I used a few tricks like "destroy HQ mission". I was a(guess what?) space marine and fighting with an eldar. And I was playing the original Dawn of War with no add-ons/mods/patches. Sooo bloody....I've killed like two or three Avatars before I deep striked 3 dreads and two squads of terminators in his base and blasted to hell that Webway assembly.
On Winter Asault or Dark Cruasde it's harder...not impossible...but very difficult.

On Winter Asault or Dark Cruasde it's harder...not impossible...but very difficult.

....one word....Whirlwind. It's a divine tank when facing massed infantry(especially orks). By the way...also try using the librarian's "word of the emperor" power when charging into close combat. Your troops will be immune to death for two minutes or something like that. Very useful to turn the battle around. Also bombard the place where you know they usually attack....or place mines in that place. Won't kill them...but will surely weaken them.
) but you have to take advantages of a few things like "arrange" your starting position in an isolated area, and "fix" your opponent's location so that you know where to attack when you have the forces. Also never play on an 1 vs 1 map. That's simply insane
. And know whom you're fighting against....eldar/imperial guard/orks means heavy bolter, chaos, necrons, tau means plasma gun. Use the frag grenades as much as possible. I also never leave home without a flamer on each squad and two scout squads with snipers(low morale on enemy infantry is always welcome).
. The whole air units thingie wasn't necessary....they should have sticked to bringing one new unit type to each race.