I tried doing it without harvesting at first but it was almost impossible to kill the big daddies in the begining. I harvested a couple but was still dying a lot.
So I restarted, decided to not harvest the first one. They gave me a teddy bear on the next level with a mind control plasmid that made the big daddies think I was a little sister.
Soooo... I would tag one, find another one, let them duke it out (While I took pictures), and basically breezed though the first half of the game doing nothing really but letting the Big Daddies do the heavy lifting while I took photos of the carnage.