All of the achievements mentioned above can be earned in a single game of Classic using a small exploit of sorts.
PAUSE, THEN GOOGLE TRICK:
Basically, for every question, as soon as it pops up and all answers are visible, hold down the back button on your phone. This will pause the game, bringing it to the app switching screen with the question still visible in the shrunken image. While it is in this mode, the game is paused, but you can still read the question. Now load up Google or your favorite search engine and start researching the question. Most can be researched in less than 10 seconds with some well-chosen keywords. When you get the answer, tap on the games shrunken screen. Click "Resume" and input the correct answer. Use this method for every question in the game.
STEPS TO GET ALL THE ACHIEVEMENTS IN ONE GAME:
When you are first setting up the game, disable both the medium and hard question packs. Make sure to turn Wedges Needed to 6, Wedges Earned On to "All Tiles", no AI opponents, and the Time Limit to 15 seconds. These settings are optimized for what you are about to do.
First just move around the board answering questions of the correct color to fill up your pie. Do this all as quickly as possible as one achievement is related to finishing in less than 10 minutes. Particularly try to roll the die and move your pie around quickly.
Once your pie is full you can move into the middle area of the map (NOT the center piece, which will end the game). Keep answering questions around this area until you get "Absolute Genius or Cheater" for answering 15 questions right in a row.
Then, as quickly as possible, move to the very center and answer the final question to win. It may take a few turns as you need to roll the correct number to land there.
If you didn't miss any questions along the way, and did it in less than 10 minutes, you will have gotten 12 achievements.