The description says, we can earn it by:
Provided non-wiki answers of 15 total score in 20 of top 40 tags
Does it mean a 15 score in each of the tags, or in cumulation?
It's definitely not 15 total score across all tags.
According to the List of all badges with full descriptions, it requires a cumulative answer score (all upvotes minus all downvotes) > 15 per tag in 20 of the top 40 tags:
Also! Be aware that the Generalist badge requires the site to have 200 questions in each of the top 40 tags before anyone on the site can get the badge (from http://blog.stackoverflow.com/2010/05/generalist-badge-implemented/):
It's 15 score per tag, in any 20 of the top 40 tags. I'm not even sure the other interpretation makes sense; you could end up with 15 score in one tag, and the "20 of top 40 tags" part doesn't do anything