Find the remaining side of your waterproof connector. Slide the included cover nut onto the cable with the open side toward the connector, as shown.
Slide the white nut from your cable gland onto the connector facing the other direction, with the open side toward the bare wires.
Open up your GoPro case. Use a 15/32 (12mm) drill bit to drill a hole in the side of the case next to the on/off button. Get it as centered as possible so the nut has room to screw down flush with the case. I found it helped to drill a smaller pilot hole first to keep my drill from wandering.
Screw your cable gland's main section firmly into the hole as shown, with the shorter side on the inside of the case. Thread the included plastic hex nut onto the outside and tighten it with a wrench.
Slip the bare wire end of your waterproof connector into the cable gland from the outside, making sure not to dislodge the foam insert. Adjust it until just the bare wires are sticking out, with the main part of the cable inside the gland.
Double check that you've got both connector nuts on your connector: the white one from the cable gland, ready to screw to the case, and the black one that came with the connector, ready to screw to the male end of the connector.
Once you're sure it looks right, screw the white connector nut onto the cable gland to lock the connector in place. Tighten with a wrench.
Grab one of the male connectors you cut off your LED strand. I extended the wires a bit on mine using silicone stranded wire, which is less likely to break when it's flexed a bunch.
Solder the 3-pin NeoPixel connector to the wires on the waterproof connector. Trim the yellow wire since we won't be using it. Connect white to white, red to red, and black to black. Cover the connections with heat shrink and solder.
The LiPoly battery has a metallic covering, which could potentially cause a short if bare wires touch it in a confined space. It also has delicate wire connections at the top, which will break if they get flexed too often. I avoided both these potential problems by covering the battery in electrical tape, making sure to carefully tape the wire leads down to the side of the battery so any strain will not be put on the solder joints.
Place the battery on the bottom of the case. It should fit snugly. Plug the NeoPixel connector into the QT Py and nestle it on top of the battery. Make sure everything fits below the level of the lid -- if you have to squeeze or force the case closed because the insides are too big, your case will leak. This is not a huge deal in most environments, but if you're going to be getting wet, you want a good seal.
Be sure you can easily access the on-off switch, and also the battery connector, so you can recharge the battery without pulling everything out of the case.
Plug the case into your LED strips with the waterproof connector, double check that the gasket is in place, and screw the cover down. Turn your lights on with the on/off switch and gasp with delight.
Assemble your costume, use WLED to make some magical animations, and then go out and light up the world.