Mike Holmes is great. He basically is taking the staggered wall that was built between the two "townhomes", put insulation in there, put putty pads around the outlets, and then QuietRock. QR is pricey for sure, but they nailed how it works. Two layers of drywall for the outside "sandwich" with a sheet of thin metal coated in a polymer. This is the same as doing two layers of 5/8" drywall yourself but before the second layer, you apply GreenGlue. The GreenGlue method can be a tad messy, but it is a lot easier hanging single sheets of drywall than hoisting up that QuietRock. Plus, some argue that GreenGlue with the two layers of 5/8" drywall is actually superior, and a lot cheaper, than QuietRock. What they show in the video is pretty much what I did in my theater and I have had amazing soundproofing results. I hear the tv in the living room next to our bedroom way more than any movie played in the theater right below our bedroom. Of course, I also had a door and air ducts to deal with too.
What you want to go for is three fold. 1 - decouple the common surfaces with a double studded wall or staggered stud wall. 2 - provide absorption with the insulation in the wall cavities. 3 - provide dampening with mass and elastic polymer via the mass of the drywall and the polymer of GreenGlue. Of course Plus and "holes" like they did, and you will be set.
Unfortunately, this means either building a whole additional stud wall with at least an inch gap between it and the current wall, or tearing it out like Holmes did and starting fresh...
