This one is relatively easy as you don't really need to do anything for it.
Go to Online mode, create a match of your own and turn on Quick Mode, and start a game against bots.
You don't even need to play the games. They can just be left on in the background while you do other things. Your controller can be turned off safely, as it keeps the games running anyways. You can also just do this when you go to sleep/work/any activity that takes a long time if you want, as the game never stops to ask if you're still playing, or kick you out.
The game automatically starts a match again, 60 seconds after it's over, so you don't even need to watch for a game ending.
The achievement should automatically pop after the tenth match, which can vary in length depending on your in-game level. If you're level 1, for example, the AI takes a long time to buzz in and usually gets the first (or even second) guess wrong, making it take longer. If you are at the maximum level (40), the AI never misses a question and will buzz in within two seconds. So depending on your level, it could take anywhere from a guesstimated 90 minutes to a few hours.
And on that topic, you can also use this method to (slowly) grind level-ups too, for the Jeopardy! Master achievement, while you're not actually playing. However, if you try this level-up method in offline mode, a game will not automatically start again without human input. So make absolutely sure it's an online game.