First, find out what you're up against. Does this foundation have a raised footing around the outside? How thick is the slab? Spend an hour or less with a shovel, and dig around it to find out what's really there. If it's just a fairly thin slab, it should be easy to get rid of.
Breaking up a slab with a sledge hammer is easy if you can use some leverage to get the slab up off the ground just a little way. I just finished a job where I moved some 8' x 8' slabs around using a small hydraulic jack. Yours probably weighs about as much as a car, so you might be able to lever it up with a 10 foot hunk of large water pipe, or lumber, or something. Then just throw a couple 2x4's or whatever under it, never put your hands under something like that, and you're ready. Sledge hammer the parts that are up off the ground, and it'll break quite easily.