Start it off by putting it between two barrels or two sawhorses a foot or two apart and whcakcing it with a sledge hammer. Then put it back in place and whack it along the smae break line.
They make Wiz snippers, or something like that with 3 letters, that have increased leverage, but I thought about them before and something makes me think they wouldn't work better. They have shorter jaws and maybe they are thicker, and the thickness would interfere. They come in three colors and you don't want the yellow ones, because the handles are right behind the jaws, and they are only good for short cuts or cuts where the material bends out of the way of the snips.
Oh, you want to do this before you r3emove it. You only said this:
"I >do not want to expose the whole thing all at once. 1/4" plywood is bendable but not very easy to break. "
Why don't you want to?
Next time start with the whole question and the circumstances, so we don't waste time.
Do you have another bathroom. Even if not, you can pull the whole thing up, then lay or use a couple nails ton put scrap plywood down to walk from place to place.
If I'd known that part of it was still nailed down, I would have said to use a crowbar, or a 2x4 for crowbaring. When it's up part way, put your back against the tub and use your feet to make it go farther. When it's over 110 degrees up and over, stand on it to make it break. Or better yet use the circular saw or sabre saw first.