Courtesy of xbox360achievements.org:
From the Xbox Live multiplayer options I recommend creating your own game on either course with random levels and set to 4. This will make the matches go much quicker as you'll be playing on only 4 holes rather than 9 or 18. I also recommend doing it on the Caribbean as they tend to shorter holes and thus end faster.
When it says to beat 10 other playes it doesn't mean win in 10 seperate matches, it means to be better than 10 players total (can be the same person.)
E.g. if you play a four person match and get second you beat the third and fourth placed people and get two of the ten necessary wins.
Good luck and see the achievement "Parkland Challenge" for general tips on how to play the game well.
Also, if you've got extra controllers you can simply sign them in as guests and then beat them for a quick win in the online.