Beautiful Katamari

Obviously it's clear what you have to do for this achievement, so let me tell you where you have to go since the game's interface can be a bit confusing. You're going to want to be on the main island that you start out on when you load the game, and go over to the right side of it and pick the space ship. This will send you to another menu where you can choose quick match or whatever. If you don't have a boosting partner, search for a planet. If you can't find one, create your own.
Only the planet owner can start the match, so someone who is afk is going to be useless to you. The switch is on the middle left, it's like a mushroom. Hit it and the king will start talking.

Press the start button to skip through his sets of words. The planet owner can choose the level. The one to the far left is the fastest to play (1 minute). The person with the most of the item required at the end will win the game. You do not need to win for this achievement.