Sadly, in these circumstances your best advice is not to throw good money after bad - do not spend your own money taking them to Court (if your Union is paying that's another matter) as you are unlikely to get anything back.
The only qualification I would make is that if you are absolutely sure she is actually financially secure, is working & you have details of her bank account (did you get the account number & sort code from her when she did pay you?) then once you have a CCJ & she defaults on its terms you might be able to get a third party order to take money direct from her account.
However, even this is dodgy - she could close that account, or she could provide the Court with (fictitious?) financial details & a nominal payment offer (eg £1 per month) when you issue the Court claim. If the Court made a CCJ for her to pay only the £1 & she did so without fail, then you would not be able to take any other action.