How to change child's surname

I am a father of a 3-yo daughter. She is living with me and I am responsible for everything, so I guess I'm like a single parent. The mother of my child and I aren't really in good terms but she has no choice about this arrangement because she's still in school. The thing is, she doesn't even text, call or visit anymore, even just for the sake of her kid and she is aggressive towards me if I'm the one who tries to initiate a conversation. Now I have enrolled my daughter for nursery school and one of the requirements is a birth certificate. Unfortunately, I am not in the birth certificate as I was not present during delivery (but I was able to go 2 days afterwards; birth was in Bicol, I was in Quezon City for work and had to secure the necessary leave passes that's why I was late). I have already given her the documents to have me recognized as the father in the birth certificate a couple of years ago, but since she is such a warfreak and is selfish she did not submit the documents. I have appealed to the mother's mom about this and she said that she will be the one to submit the documents, but that I have to give her new ones because the previous ones may have been lost already.

My question is, what are the necessary documents that I need for this? Can I get them even if I'm now in Leyte, and my daughter was born in Bicol?

Also, I remember the first time we asked the civil registrar about this, he mentioned that the process would cost P4,000+, but I found a website that talked about RA 9255 and letting an illegitimate child use her father's surname and it would only cost P1,000. So how much will I really be paying?