I started by purchasing and taking apart a Magic 8 Ball.

Many people on the Internet will tell you that this isn't that difficult.  "Run a knife around the seam and then gently pry apart," they'll say.  "Use a flathead screwdriver and plexiglass knife to gently separate the two halves," they'll say.

The Internet is full of lies.

I spent two days using various knives and razor blades on this thing.  Finally, I broke out my Dremel tool.  Or I should actually say I broke my Dremel tool.  Only four of the ceramic cutting wheels, mind you, but I broke four ceramic cutting wheels getting this thing apart.  Mattel does not want you getting inside.

Check out the image: there's half a centimeter of plastic to cut through here.  Anyone who does this with a razor knife is either more patient than I am or a stupendous badass with arms of steel.

Once I cut through it enough, the halves separated cleanly.