I think that achievement should be like this :
You must have 6 kills, 6 deaths, and 6 assists at the same time. (For A Sign of The Devil, 9/9/9 for Eye'm The Strongest)
So, if you have 7 kills, 5 deaths, and 6 assists then you died, you won't get the achievement.
It applies at one point, so if you have gained the requirement, you get the achievement. Not at the end of the game.
The difficulty level should be raised if you make it at the end of the game