I thought I would add this just in case others are having some issues with getting this to pop. I had this achievement glitch on me, and you can see that this was the very last achievement I got on this game to complete it 100%.
I completed the game first - all but this achievement. Then....
What I did was start a new save file on a flash drive. The game requires you to play Act 1 and Act 2 of Green Hill before it opens up. I died on Act 2 one time (I jumped over the bumper and fell to my death). Then I went back and played Act 1 until I had more than 100 kills - the achievement still did not pop.
I then deleted the save file on the flash drive and started another new game, new save on that same flash drive. This time I played Act 1 and Act 2 of Green Hill and did not die at all. I then played Act 1 until I had 100 kills, the achievement popped this time. In fact, the achievement popped in the middle of the level. I did not even have to finish the level for it to count.
So it appears that dying before you get the 100 kills is a problem. It may be THE problem, but I don't know for sure. Maybe it is not just dying but dying by falling to your death. I am not sure. But if you are having this problem, if you start on a new save and don't die, you should get this achievement.
I had read the comment by LitaOsiris on another solution and how they just played Act 1 and Act 2 until they got the achievement as well. So I did the same thing and can confirm that it works. Of course, I died on my first attempt.