government procedures do take some time..why have you not checked this while submission at school.
anyways,the procedure is different if it is within the first year of birth registration and issue. since this is very long, this is my guess (take the opinion of an good advocate)
Prescribed application form duly filled.
Requisition letter from parents stating that their names are pronounced wrong in the certificate.
All previously obtained birth certificates in originals.
Hospital correction letter if the delivery was at hospital.
Evidence proof for name of father or mother (ie., education document or service records)
Xerox copy of ration card.
if you have a sibling and if their birth certificate has all the details correct, it would help.