Extending User-Badges Module

Use the Rules module. User badges creates an action to assign user badges to a user and, using the Rules module, you can make this trigger on a huge variety of conditions. If you need more conditions, you can just contribute extensions to Rules and the framework is all there.

I see you are using 5.x. I think the closest thing to Rules is workflow-ng on Drupal 5. Rules is a Drupal 6 module. But User Badges is also more actively developed on D6 so, if you plan on making badges a significant part of your site's functionality, I think you probably want to migrate up to Drupal 6.

I think Userpoints Categories has most of what we need. What we are trying to do is assign multiple badges for multiple types of points: points for logging in, points for posting content, etc. Is there a way to use the UserPoints categories to do this? i.e. create a category of points for only logging in, and to assign badges not based on "uncategorized" points but instead on the specific category of "number of logins"?
If we use the Rules Module, we can use trigger events to add only to the "uncategorized" points still, not specific categories.

Thanks again for any help.

You are really getting into the details of the interaction between Rules and Userpoints there. Maybe you need to add a feature request for Rules or Userpoints, or maybe ask on their issue queue, but this thread is for issues with this module and your question is well beyond that scope now. I don't have the knowledge to properly answer.