The only way to get the airport tax refunded on Wizz, is for flights departing or arriving in Germany. Again, you can't or they'll just ignore you.
I've used a website from Germany specialised in this (google it: Geld fuer Flug). It takes just 2min to fill in the request, and they will get back to you if it's successfull or not (1-2days from personal experience). They don't specially exactley (they'll take their comission from the tax, around 20-30% probably).
The only downside that they don't specify on their FAQ, even though you sign that you agree with their terms from you mobile (when accepting the offer they make you), they still need to send you the papers for you to sign (transfering the ownership of the airfare tickets from from you to them). And they only send those papers in Germany, Austria or Switzerland (they provide for envelops, stamps all the thing required to send them back). So if you're living there, or have someone living there, they can assist you with this ;)
You can go back for the last 3 years to ask for the refund.