You don't. You let the IRS do it.
Do the following: Send her a W-9 (link below) by registered mail, or Priority (so you get a tracking number).
Now, when the IRS contacts you and says, Hey, you didn't enter the SSN#, you can write back and say, I tried but she refused to provide this and here is my proof (attach a copy of the postage, the letter saying please complete the W-9, attach any emails, and that sort of thing--you may even want to hire a process server if the amount is over $5K) and send those receipts off to the IRS. They will take it from there. Trust me, there is no where to hide anymore. The good thing about that is, it's getting harder to screw over honest people.
https://www.irs.gov/pub/irs-pdf/fw9.pdf
