Yes, I got a little worried when I only had one enemy left to fight but the list told me there were more. But then the number did change to 60/60, so all was good.
What I would have preferred is that I get a bonus when I killed all enemies regardless of whether I kill them all before I get the ring or after. Several times I missed a couple of enemies on the way up, and killed them after I got the ring, but I didn't get the bonus.