What is the best way to publicize the existence of a fraudulent journal?

Send it to one of the successors to Beall's list of predatory journals. Their websites:

• Cabell’s whitelist/blacklist: commercial, subscription required for access, but accepts listings
• Stop Predatory Journals: open-access, crowdsourced via Github, successor to the now-defunct ScholarlyOA site
• Beall's original list: now being maintained by an anonymous European postdoc

There is little point in publicizing a particular fraudulent journal. It costs very little to set up a fraudulent journal. If people become aware of one fraudulent journal, criminals will simply create a new one that is little known.

What is useful is for academics to treat all journals as fraudulent until they have evidence otherwise. Teach your students (if any) to be skeptical. Teach them to never pay money to low-quality journals, even if they are not fraudulent.

(Gathering evidence that a journal is not fraudulent is easy; just read the journal. If it has good contents, it is a good journal. If the journal has bad contents and is not fraudulent, don't publish there anyway.)