You can burn through this Achievement in short order with the help of a second controller. Frenzyfest tournaments earn you 100 points for every round you win, and when playing against a dummy controller, you're guaranteed to win every round, barring any extremely bad stroke of luck.
Set up a seven-round tournament, followed by a three-round tournament and you'll compete in the ten rounds that you need for the full 1000 Party Points. The load time between events in the tournaments is quick - faster than setting up individual events from the menus.
Some of the events are really quick to complete, but some may require you to endure a full 45 seconds to one minute before they complete. Either way, you should easily be able to knock this off in under 10 minutes.
If the Achievement does not pop right away, try loading up party games and the achievement should probably pop as soon as the first game has loaded. Thanks to vSully
for that helpful tip, and to SweetArkhane
for bringing it to my attention to include in my solution.