Ok, I finished the first level with both Not Detected and Killed No One. The only issue is the game only gives you a status on these two efforts at the end of the mission. I had to redo the first mission, being a lot more careful, because apparently I was detected once, but I've no idea where. So I have to, while playing, be aware of the ingame chime that signals I've been detected.
@Philistine;: Do you know if I can do this differently? Any way to find out if I've already been detected mid mission? I'd hate to a long mission and only find out at the end that I was detected, and failed the achievement.