I've just encountered my first Elite guard. My companion says something along the lines of "That guy looks tough, you may not be able to take him down even if you catch him by surprise. You'll have to stun him somehow first." Looking in my bag of ninja tricks, I couldn't come up with a way to "stun" him other than beating the snot out of him, which obviously attracted his attention. Is there anyway to kill him silently?
Elite Guards are the first of a couple of different types of enemy that are immune to instant-kill quick-time-event attacks.
That said, you can "stun" them and then instant kill them with certain equipment:
You can outright kill them with:
You can also lure them into traps or drop environmental objects (ie, chandeliers) on them to kill them. Or you could terrorize nearby guards and get them to attack everything, including these guys. I don't believe they themselves can be terrorized, though.
Elite guards must be disabled, a special status effect granted by poisonous smoke bombs and caltrops, before they can be killed silently. Often, it is easier to use distraction items to get past them, but that does not mean silent kills are un-doable.