The problem here is "score" is not necessarily the number of up-votes gained, but the sum of up and down votes.
You can't call it "vote total" because that could be interpreted as the total count of all votes (up and down).
You can call it "vote sum", but that's weird.
It can be called "Vote Score" and then defined. That might be better.
I'd also go with replacing "or more" in every description with a + sign after the number.
Proposed re-names (note complete revision of Populist):
Nice Question
Question with a vote score of 10+
Good Question
Question with a vote score of 25+
Great Question
Question with a vote score of 100+
Student
Asked first question with a vote score of 1+
Enlightened
First to answer and accepted with a vote score of 10+
Generalist
Provided non-wiki answers with vote scores of 15+ in 20 of the top 40 tags
Guru
Accepted answer with a votes score of 40+
Nice Answer
Answer with a vote score of 10+
Good Answer
Answer with a vote score of 25+
Great Answer
Answer with a vote score of 100+
Populist
Answered with highest vote score outscoring by double an accepted answer with a vote score of 11+
Reversal
Provided answer with a vote score of 20+ to a question with a vote score of -5 or less
Revival
Answered more than 30 days later as first answer with a vote score of 2+
Necromancer
Answered a question more than 60 days later with a vote score of 5+
Self-Learner
Answered your own question with a vote score of 3+
Teacher
Answered first question with a vote score of 1+
Tenacious
Have 6+ accepted answers with 0 vote score; must be 20%+ of total answers
Unsung Hero
Have 11+ accepted answers with 0 vote score; must be 25%+ of total answers
Pundit
Left 10 comments with 5+ vote score
Tag Badge (Bronze)
Have total vote score of 100+ in at least 20 non-community wiki answers to achieve this badge.
Tag Badge (Silver)
Have total vote score of 400+ in at least 80 non-community wiki answers to achieve this badge.
Tag Badge (Gold)
Have total vote score of 1000+ in at least 200 non-community wiki answers to achieve this badge.
Disciplined
Deleted own post with a vote score of 3+
Peer Pressure
Deleted own post with a vote score of -3 or less
Sportsmanship
Up voted 100 answers on questions where an answer of yours has a positive vote score