This is one of those jobs where you really hope the original installer took many shortcuts and did a crappy job, thereby making your job easier.
Unfortunately, the best way I've found to take up tile and backer board is with a prybar and hammer. Remove a tile or two, then start working the prybar under the backer. As you pry up, use the claw of the hammer or a second prybar a few inches away to start pulling up a larger section. With most backers, the screws/nails will pull through and the backer will come loose.
It's not likely to come up in big sheets, but rather in one or two foot squares, if not smaller. I did 55 square feet over hardibacker a couple of weeks ago and it took about two hours to get it all pulled up, the nails pulled, and everything hauled out. The installer didn't use thinset under the backer, but used construction adhesive instead. I used a chisel to scrape the glue off.
If yours has thinset under the backer, you might try scraping it off. If that doesn't work, or if it seems like it's going to be a nightmare, you might be better off replacing the subfloor altogether.
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Kevin
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