There is no real easy way to get through concrete! Anyway that you do it is going to involve lots of manual labor and a big mess! A saw will leave you with a square hole that is going to require you to mix up a few bags of concrete to fill in after the tub is in place. A saw will make the cleanest cut and create the least amount of mess initially, you'll still need a hammer drill of some sort to break up the piece and remove it.
http://www.milwaukeetool.com/webapp/..._192178_192137
One of these drills, rent or buy, will prolly be the best way. Your basement slab should only be about 4" thick. Mark out the whole, a little bigger than needed, and use a small 3/8-1/2" drill bit to drill a bunch of holes about 1"apart along the line, and some random holes in the center the more the better. Then switch the drill to hammer mode with a chissel bit and hammer away! Make sure you wear eye and ear protection!!! You will have a mess to clean up as well. These drills work great though and should require to much effort drilling.
I have never had to make such a hole in a basement floor but doing commercial HVAC I have cut many holes through brick and concrete walls, and drilled many holes for anchors.