Make sure you get the Cobra grill (or grill delete kit) as well. It's mostly the same parts that come with a Mach1 delete kit with the exception of the big black plastic piece.
The side brackets (2 bolts per side) are pop riveted onto your stock bumper. The trick is, you need to take them off your stock bumper, but you don't NEED to pop rivet them onto your new Cobra one. You just have to get the side lips (not seen when installed) of the bumper over the black brackets so that you can bolt the bumper against (not to) the fenders.
There are also two plastic clips at the bottom (1 per side). Those pull staight down and out. It also helps to remove the headlights.
I'll attach a picture of the brackets riveted to the stock bumper. It helps to turn the wheels depending on which side you're working on.