German Magazine Client not paying (US Freelance Illustrator)

As a US citizen or business you have practically zero ability to forcibly collect from an international client. You would have to use laws local to the client for any collection. And, adhere to any stipulations regarding foreign demands. It's nowhere near as simple as simply filing suit or hiring a collection agency.

You can try some international B2B collection agencies (simply Google that). They typically cost much more than local collection agencies, but that's probably your best shot.

Typical collection recourse offered in one's own country never travels/works across borders. Laws vary from country to country and a German business is not obligated to adhere to US laws regarding collection. The best you could hope for is some German law which you could possibly use to aide collection. For example, the UK has some decent laws regarding collection if you can prove the debt. I do not know if Germany has similar laws. This is where the international B2B collection agencies come it, being familiar with laws in various countries and what can or can't be used for collection.

This is a major reason I always demand payment up front from any international client.