My Tagalog is bad. I didn't understand the problem. If the biological father agree, he can pay support WITHOUT a legal decision.
If the biological father DISgree, you still have right to support, but then you have some problem:
1. He isn't at the birth certicate, so it need to be proven he is the father.
2. DNA test is expensive. And it's a problem to get the sample and SURE to be his, by he is abroad.
3. He is abroad, which make the Philippines don't have juristiction (if the ship don't belong to a Filipino company). But there is some chance a foreign company agree volontaringly to assist forwarding a part of the salary.
Is his familiy from same/close Barangay?
FIRST try to get a volontaringly agreement.
If that don't help, you can ask if the Barangay Captain take such case. (He is suppoused to when both are from same barangay, but I don't know when one is abroad.)