The thing about the Cthulhu mythos is that in the Lovecraft stories, while people dealt with horrors from beyond space and time, they weren't always wusses about it. The case of Charles Dexter Ward has a group of hardy souls braving the subterranean lair, and has someone eventually taking down the big bad with some magic of his own. Even The Call of Cthulhu has the titular eldritch horror getting rammed by a ship.
Now, shadowrun characters are a tougher breed, because strange-looking ectoplasmic beings, shaggy creatures silhouetted in the moonlight, and shambling corpses with mouths of jagged teeth are something they already deal with. Sometimes the aforementioned things consider the shadowrunners to be the horrors.
For Shadowrun, the best you can probably do is more like the movie Aliens, where everyone was badass and had big guns, but were still wigging out because they were dealing with unknown, cunning, dangerous enemies that could not be predicted or reasoned with. You can get a similar effect by having their enemy be mysterious - if they don't know exactly what it is or what it can do, then they will be more frightened of it, even if it is nothing more than a standard spirit with a palette swap.
However, I would echo the advice from a similar thread on another board, and say that if you want to do this, talk with your players first. If the group doesn't get in the mood for it, then it will all fall flat. It just takes one person cracking jokes, or complaining about GM railroading, to ruin the mood.
