Fire works well on prickly pear if you are in a situation where you can do a controlled burn.
This would be the quickest way, especially if you have a tractor with a FEL (front end loader) . You have to get every leave though as they will sprout if they touch the ground. That is where a FEL works good, scoop up and put on a wood pile. Any piece you miss, will grow, so be thorough. Even if you have to wait for more wet weather, that is ok, it will allow the cactus to dry out and burn better.