I asked my fiancee about this - she is totally at a loss to understand how this could have happened.
She suggests that 1) perhaps the gf was actually named 'Baby Girl'
2) she may not have been properly registered, and should go to NSO in Cebu or Tacloban herself, for a late registration, which will NOT require a lawyer - that is probably her best starting point.
3) if she DOES have erroneous entries on the birth cert she may well have to use a lawyer to petition the regional trial court where she was born. It seems that in this case a lawyer may well be needed.
Please feel free to email me directly if you need any more info.