Honestly, the back of the birth certificate can be confusing talaga! From what I know, you need to fill in the parent's information, legitimacy status, and sometimes attendance details ng midwife or doctor, pero it really depends kung ano ang specific form ng municipality mo kasi may slight differences per lugar. I'd suggest you go directly sa municipal health office or civil registry window para sure, dahil mas better na intact na lahat ng details kaysa mag-hassle pa later when you need the cert for school or passport applications, you know?