Use a tank! They're great for churning up the soil and you can get them surprisingly cheap at the Army Surplus Store.
Be careful, though; sometimes the used ones still have previous operators lurking inside! Before use your second-hand tank, have your friendly neighborhood Hangman clean it out thoroughly.
Simple! The answer is a point-tata-ed blonde.
Strap one of these Vicki Vale wannabes onto your tank treads, and watch as those wire-rimmed push-ups, pointy shoes, and teeth-filled shriek-holes simply tear up the turf. Remember, you'll need to change them after every few uses; nobody wants to plow with a dirty hoe.
Besides, hoe-girls are cheap. Certainly cheaper than tanks. Arm yourself with some of these bullet-bra babes and tank-gardening will be a truly harrowing experience.
Help! My backyard plantings were doing so well. But now it's infested with Japanazis! What's a victory gardener to do?