Somehow you need to get Batman.TestCase (and your application code) loaded by Karma. What I've done before is (gulp) point Karma at my development server, where it can get compiled assets. Maybe it ain't perfect, but it works.
Here's an example snippet for your Karma config:
files: [
'spec/javascripts/**/*.coffee',
'http://localhost:3000/assets/your_app.js', // loads application code
'http://localhost:3000/assets/extras/batman.test_case.js' // point to wherever TestCase code is!
]
Also,I wrote up a bit about how I've done it before (with Jasmine), in case that comes in handy: http://rmosolgo.github.io/blog/2014/01/18/batman-dot-js-testing-with-karma-and-jasmine/
As mentioned there, Batman.TestCase is an "extra", so you'll have to include it "by hand". It's not in the distributed version of Batman.js
Does that help at all? Good luck!