*** Sorry, folks -- servers are down, so this achievement is unobtainable. Original solution follows. ***
You have to win 10,000 Player Points by playing GamerNet online challenges. You can win these points either by selecting challenges through the LIVE portion of the game, or by beating the Instant Challenges that pop up during normal gameplay (if logged into the EA Servers). All count to the same "bucket" of points.
There are two common theories on how to rack up these points fast:
1. Play a lot of long drive challenges (quick, low-difficulty);
2. Play 18-hole challenges (takes longer, but gives a ton of points).
I played the game a bit before I went after this achievement; I was at around 1500 points when I started. It took me two 18-hole challenges and three long drive challenges to get this. (I got almost 4000 points from one 18-hole challenge, the long drive challenges were ~100 each.)
When selecting long drive challenges, look for those with the most points for the least distance. You have to get this on the fairway, but often the first cut of rough counts (in contrast to the "Fairway Drive" money bonus in-game, which must be in the fairway proper). This allows you to be a bit more aggressive, as rolling off the fairway does not always prevent you from beating the challenge.
When selecting 18-hole rounds, look for challenges on Pro difficulty -- these seem to have most points relative to the difficulty. (Tour Pro is best for points, but without the putt preview ability, these can be formidable.) I recommend most the challenges with high numbers of birdies and moderate birdie streaks; also, challenges with very high GIR or FIR requirements can be manageable, as long as you tailor your gameplay to match (no maximum wailing with drives, no going for the hole on every approach).
As always, selecting challenges that have not yet been "Busted" is key, as unbusted challenges give you double points.
Alternatively, you can simply keep playing the normal game modes (PGA Tour Season and Tournament Challenge) and eventually you'll get this. It will come in little drips and drabs of about 30-40 at a time (the typical value of the Instant Challenges).