I have 4 non-wiki answers to questions which are accepted and also have a score of $10$ or more. These are as follows:
But I have earned the Enlightened Badge only $3$ times.
Can anyone explain this? Is this a bug?
The description of the badge, quoted in your own screenshot, says in part "First to answer".
For one of those questions, your answer was 3rd to be posted, as the question's timeline shows.