Per US Dept. of State what you have should be sufficient provided it has your mother’s name on it as well (not only your father).
Your lawyer may not be informed on Nigeria circumstances and the 1992 Law Act #69 which only made compulsory registration of births and deaths via National Population Commission a requirement and could be using other countries situation for reference.
Most Nigerians use only what you have for legal proof of age, parents relationship, and immigration petitions. If you have other physical evidence (childhood pics, parent’s marriage cert, school records showing her name as your parents, etc) you can include them too as supporting doc.
If the US needs a DNA proof of relationship for I-130, they will certainly send you RFE but it won’t be because of your NPC document. See the link below: https://travel.state.gov/content/travel/en/us-visas/Visa-Reciprocity-and-Civil-Documents-by-Country/Nigeria.html
