Anyway, I had a sector in Drox where I was fighting for one race or another and suddenly the Shadow showed up. I don't know if their colonies were cloaked or something but suddenly they're everywhere, have like 10x as many ships as the other races and keep gaining ground. Fortunately I managed an econ victory shortly after that. In another sector I was fighting the Drakk and they had a lot of high level defensive techs so killing them was a sloooooooow, arduous process and when I killed one colony another sprung up elsewhere. The constant nuking of colonies drove my fear rating up and so I won the Fear victory before making any real inroads against the enemy.
I have noticed the Shadow will either really sink or really fly in my games. A lot of times they get picked on by most of the other races and get killed off early, but every now and then they pull off a very devastating win like the one you describe.
I also notice they're sometimes a bit tricky to keep in your alliance when you're going for bigger diplomatic wins, as they sometimes flip out and suddenly decide they want one of your member races dead. If I'm going for diplomatic win with a lot of races I often try to pull the Shadow in last if I'm going to at all.
I have run into similar situations going against races with high defense or higher techs in general. It often helps to get more races hostile with them (the more the better) to wear them down somewhat.
Another thing that also helps is espionage. If a race has better tech than everyone else then sometimes you can get a lot of nice tech out of them by going in, quickly stealing it via espionage, getting out, then selling them to friendly races to even the odds a bit. Also, if their advantage is mostly defensive and you can get your allies more even with them on that then the friendly ships will be able to hostile ships occupied longer, so if they're still hard to crack afterwards then you can follow up with some sabotage to soften them.
Of course, occasionally a bunch of ships from a "high tech" race get destroyed and you get lucky and: