For the OP, just keep shooting people with your handgun. You've got to be relatively fast but there are some enemies which you can bypass in the diamond formation sequence. It's one-hit kills in this area so don't be picky about your aiming, if you can get the guy in the leg or hand, take the shot.
When doing the sneaky bit in the first mission it's easier if you just read the spoiler below!
As soon as the stealth section start crouch and move right, shoot the guard there in the back of the head and then return towards the starting position, head left around the back of the girders and car then dash into the building. Climb up the ladder and carefully move forwards along the walkway. Stealth kill the guy up top and then take cover in his position. Look towards your objective and there's a lone guy up there. Pull up your sights (MMB on mouse, Right stick on pad) and headshot him (mark him with Q/RB if it makes it easier for you) and then simply stay crouched and walk all the way to the exit.
Alternatively, if you want to complete the area challenge, here's how.
Follow the above steps but instead of going to the exit, move half way up the rooftops on the left and look down on the group of 4-5 men below. There's a cluster of three, carefully aim a grenade to land between them and then pop out and shoot the others. If you time it right it'll explode just as you shoot the other guys and the little pop up that says you've been detected won't count. Challenge completed.
[Edited by WskOsc, 7/3/2012 10:15:02 AM]