Enter the gross amount paid as an Other Miscellaneous Expense in the Other Common Business Expenses interview of TurboTax Self-Employed, description as "Non-U.S. Services (Philippines Virtual Assistant). You should, however, get a form W-8BEN signed by the foreign contractor.
As long as the foreign contractor is not a U.S. person and the services are wholly performed outside the U.S., then no Form 1099 is required and no withholding is required.
You should get a form W-8BEN signed by the foreign contractor. By signing Form W-8BEN, the foreign contractor is certifying that he or she is not a U.S. person. The Form W-8BEN is not filed with the I.R.S. It is kept on file with the U.S. payor in case the U.S. payor is audited. If audited, the Form W-8BEN supports why no Form 1099 was issued and why no tax was withheld.