An unofficial, but popular Deus Ex wiki says the following:
"The aim is to complete the game without killing anyone directly, or someone dying as a result of an action taken by the player. The only exception to this is the Boss fights...killing anyone in the Prologue chapter will lock out this achievement
And currently, it appears there is no way to see if you are still eligible for the achievement at any time:
"Unfortunately if you lock out the achievement by accident, unless you aware that you did so and reload an old save, there is no indication that you have done so and may end up playing through the game and not get the achievement due killing a character earlier in the game."
This seems to be a fairly sought after feature though. Since the game has been so popular since its release (over two million units sold already), I would not be surprised if a patch is released soon resolving these complaints.