Unless you have your own transport do take an organised tour. You may well be, like me, a fan of independent travel, but the "tour" is little more than a van from the city centre to the river with a couple of photo opportunity stops on the way, admission to the river, and all the assistance you might need. There's no great advantage to doing it independently. Incidentally, PP might "considered as the largest city in the country" but most of it is countryside and the river is in fact a fair distance away from where you'll likely be staying.
As for whether you need to book, that's a question which setting up the answerer up to fail. If I say no, and you can't get a ticket, you're going to be unhappy. Unless there is a PP travel agent on here you won't get a definitive answer because "it depends".
All I can say is, I didn't book until I got there and had no problem. The country isn't heavily touristed but do bear in mind that the river is a very popular spot with the tourists who do make it to the country and also with Filipinos.
My conclusion would be, book something when you have your dates finalised but don't sweat on it until then.
POSTSCRIPT: I just noticed that this is a rather old question. Perhaps you could feedback with whether you booked or not and if not if you got into the attraction ok?