I think when most people hear "juice diet" they tend to think of buying bottled juices and surviving on just those and they are really not healthy. You must make your own fresh juice in this diet and no sugar is added.
They recommend buying a very high quality juicer and juicing massive amounts of fresh fruits and vegetables daily during the juice fast. This includes all sorts of vegetables, including large amounts of Kale and other power packed veggies. Not many people would go to this trouble and would try to short cut it with bottled juices, but again that's an entirely different thing.
The two men in the movie lived on nothing but the freshly juiced vegetables for the length of their fast, and their juices contained naturally sufficient amounts of proteins due to the vegetables chosen. The diet was expensive, costing around $25 per day if organic, or about $11 a day for conventional fruits and veggies (though you'd fill yourself with a lot of pesticides with this route).
The ReBoot website, which supports the diet behind the movie, recommends an alternative route of juicing just 5 days at a time and consuming whole fruits and vegetables in between the juice fasts.
If you decide to go this route, please also follow their advice for regular monitoring by your physician.