Rent a hammer drill at your local tool rental store. They can help you with the right bit, too. You'll need carbide or diamond (your twist drills won't even come close- they will melt during the first hole).
The holes you will be drilling are large. You need a good tool.
Actually, I was thinking 2 post lift- your scissor style will have significantly less strain on the bolts (and they are probably smaller), but you should still make DARNED SURE you are installing COMPLETELY in accordance with the manufacturer's specs. Read them carefully. They will probably discuss concrete thickness, type of bolt, anchoring method, grade of bolt, etc.
It's a car lift. It can kill you.