If the birth certificate through Corporation on the orders of competent court will not serve the purpose, better skip that process.
You can apply for birth certificate with the Corporation authorities mentioning the correct date of birth, if the authorities refuse to give the same since their records show a different date, ask them to give the same in writing and after that by impleading them as a sparty and on the basis of that refusal you may file a suit before the jurisdictional civil court for declaring the correct date of birth as per the passport and the judgement copy will be sufficient to solve the purpose.