Looking at phase III of P90X2, your first question should be, "What is P.A.P.?" First of all, please pronounce it "p, a, p" - not "pap." Second of all, it means post activiation potentiation. According to the guides this is the state of the art way that athletes train. While I take that with a grain of salt, I will say that they are amazing workouts. There is a P.A.P. upper and P.A.P. lower which make up 4 out of your 5 workout days in phase III.
Basically, what these are about are combining heavy loading exercises with explosive movements and isometric movements. What I believe this does is awaken all the types of muscle fibers. For example, if you do a bunch of slow push-ups, clap pushups (for the explosive) and a plank hold (for the isometric) in succession, you are activating all three energy systems and both fast and slow twitch muscle fibers in a very brief amount of time. I'd imagine this burns more calories and has great effects on your functional fitness.
In my mind, P.A.P. Upper is the money workout of the two, P.A.P. is challenging but in some ways, since we are so familiar with explosive leg movements and isometric holds in the legs, the workout isn't as novel. It's still a killer. In phase III, you have to focus since there are essentially these two DVD's plus Yoga, and that's it, but if you follow the plan, it will get you where you need to be. One thing I am excited to try after P90X2 is the Asylum/P90X2 hybrid. I'd imagine the way the P.A.P. workouts are folded into this schedule is epic!
Overall, phase III is a solid B+/A- for me. At times, it's amazing, but there are only two workouts, it takes a lot of will power to press play on the same DVD's over and over. Like most of P90X2, you have to trust the science - more research was done in putting together these DVD's than any other, ever before. Trust and you'll be amazed!