I recommend these tools to help you, all can be found at a nationally-known home center:
- Respirator with filters that can handle asbestos. $45.00.
- 6" or larger scraper with handle which you would be found with garden tools, slegehammers, etc. About $25.00. Recommend getting one that is forged and one piece.
- Non-flammable solvent to soften/dissolve the adhesive. $10.00.
My experience is based on removing late 50's vintage 9" asphalt tiles from a 1000 sq. ft. basement.
The scraper will allow you to stand and use your legs for power in lifting the old tiles. As you go, you may gain enough momentum to blast through them quite quickly. You want to try to remove each tile intact, but here's where the respirator comes in.
The respirator is a must-have. If your tiles contain asbestos (only professional testing can make sure, but it is safe to assume they do), breaking the tiles into small pieces can liberate asbestos fibers. The adhesive may also contain asbestos, so the scraping action can present a hazard as well.
The respirator may sound expensive, but it will be the last one you'll ever need because it makes a better seal with your face, can use a number of filters for various conditions and will last a lifetime with normal care.
Assuming your cement floor is in the basement, I would try to find a non-flammable solvent since any pilot lights would present an explosion hazard. The bulk of your time will be spent scraping up the adhesive.
Also, the tiles are heavy, something like 1 pound per tile.