In nearly every car, body panels and brackets are attached using spot welds. Removing them takes the right tools and a bit of patience. Here's what I used:
Most importantly is the spot weld remover tool. It's basically a small hole saw with an adjustable guide in the center to keep you from drilling into panel underneath. Use a punch to serve as a guide to center the tool then drill away the weld, careful not to drill to deep.
Once the spot welds have been drilled the bracket should just fall off, if not a chisel and hammer will come in handy. Even with the tool it's easy to drill to deep in that case a little welding will be needed to fix the hole.