Rather restricted here but here are some challenges to try:

1) Duff your first shot then get in under or on par
2) Get a drive of over 350 yards
3) Set a handicap of 16 on the other cpu golfer in a two player game and win.
4) Complete as many holes as possible using power and approach shots only (except for putts)(I've done 11 holes)
5) Complete a round of golf by always moving the impact point on the ball the the left or right when taking a shot (except for putts)