We are remodeling our bathroom. The ceramic tile was laid using the grout not only between tiles but as the adhesive as well. It is very "solid". We have even tried beating the tiles with a sledge hammer. The bond appears quite secure. Any suggestions?

Call the big box stores, or your local tool rental yard and ask them what they have to remove tile. There are tools with correct bits designed to do that kind of work.

If it can be done with hand tools, there is a 6" wide heavy duty scraper available at home stores for around $20. Looks like a short shovel with the blade attachment.

Harder to remove tile will take an electric impact hammer with a chisel bit. This can be rented at any tool rental outlet. Noisy, but makes short work of any tile.

Why not get a cement product from Home Depot that either self-levels or you can trowel it over the uneven floor. I would do several coats, the first to fill in the main areas, then come back when it is dry and do a smoother top coat. Heck, even a third just to even it up nicely is better than renting some awful equipment and bang out the old stuff. You'll likely damage yourself along with surrounding walls, etc... with such equipment. Just mix the cement a little at a time, it sets up quickly. It's really fun, kind of like icing a big cake. Scrape down any uneven spots with a putty knife, or you can sand it smooth. Just don't wait too long as it gets harder as it cures. I would try to taper the cement down towards the doorway area but any height difference can be fixed using a variety of transition strips available. I decoupage over floors like this so there is virtually no height problem. www.decoupagefloors.com

If you leave the old tile in it will through off all you baseboards, door openings and any floors butting up to it.
If it's a kitchen and you have a dish washer it's not going to fit with an extra layer of tile.
I've never once heard or seen anyone getting hurt with a hammer drill removing tile.