I've done a number of missions with guards I cannot kill, either armored or shielded, although shielded is worse if you don't have any way to deal with it.
Like immaterial said, just avoiding as many as you can is an important strategy.
If I have to kill someone under those circumstances, I use a window or a fuel tank explosion.
Of course, if you can get a crashbeam or subverter, save those for the times when you must kill a shielded guard right now.
For armored guards without AP, they're a bit easier to deal with. Sure, you can't incapacitate them directly, but they still get staggered. So a couple wrench hits and a shotgun blast will send them flying out the window, assuming you already broke it. If you didn't, it's even easier!
Staggering armored guards is a good way to buy time even if you don't have anything to push them into. They can't attack you while they're staggering.
All perma-shielded guard personal missions seem kind of common. But 5 charges of crashbeam or subverter ought to do the trick, if you're creative and stealthy.
Don't forget, you can lure guards wherever you want them to go, without even setting off an alarm. Just let them catch a glimpse every so often.
Has anyone had any luck forcing their way in through a window with the normal pod? The windows are easy to spot, of course, but getting yourself to eject in the right direction, and then popping the window(You have to shoot the window, right?) seems tricky. But it seems like a really cool way to shortcut a mission.