Did you see the FAQ?
https://www.dia.govt.nz/diawebsite.n...Document#seven
I am not in contact with one or both of my parents. What should I do?
If you are not in contact with your claim parent, you must provide original documents that show proof of their New Zealand citizenship. This is to enable a claim to citizenship by descent to be determined, these include:
Claim parent's New Zealand birth certificate; or
New Zealand Citizenship Certificate.
Please contact us if you require further assistance.
Claim parent deceased
If the claim parent is deceased an original death certificate needs to be provided.
I suggest you email DIA and ask them about filling out the forms, they're usually pretty easy to deal with and then you'll know you've got the correct info.
I applied for citizenship by descent for my son when he was a baby and it was a very easy process, your situation is more complicated though.