Controlling destructive beetles can begin in the larvae stage of their development! These big white grubs you often find in the soil in the spring are actually Japanese Beetle babies. Controlling them organically can often be achieved by using natural predators to your advantage.
Of course, pick out any grubs you find while doing early garden maintenace in the spring and early summer and toss them into a bucket of soapy water or crush them if you see them.
Beyond that there are a few organic control methods that you can encourage in your own garden areas.
Birds are a heavy natural predator, and if you have chickens, giving them a chance to dig about in the garden in early spring will allow them to scratch up and eat many of the grubs you'd otherwise battle later in the season. The common garden ants will also attack grubs at this stage of development, as this photo shows. Parasitic wasps will commonly prey on these grubs as a food source for their young, so encouraging these natural predators (and avoiding sprays that kill them) is very helpful.