Today I've got 10 upvotes for an answer. Answer was a first answer in the question. I got an Nice Answer badge for this, but no Enlightened badge.
Shouldn't I get both?
Here is my answer :)
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It will at earliest come when the grace period of the last vote (the time wherein the user can undo the vote) has expired. As far as I know, the grace period is 5 minutes. So at earliest 5 minutes after the last vote you should get it. At least, have patience for about 24 hours. There might be some cronjob responsible for rewarding the particular badge(s).