Start out by choosing golf, single player, single hole against the rookie opponent. Choose the lighthouse bay hole. Hardest part is hitting the ball far enough away from the hole to get the achievement.
What I did was to hit my tee shot with a 4 iron into the fairway. Then on my second shot hit the ball as far to the left as i could to be away from the green, about 80 yards away. On the next shot i used the 6 iron. Practice before hitting to make sure that you can get the ball to the top tier of the green farthest away from the hole. That put me 46 yards away. All you need to do then is make sure the white line is as solid as possible and make the putt. Good Luck TA'ers
EDIT: Credit to Pinicus
Using the same strategy but playing on champion difficulty. The flag is placed on the back top tier so instead of trying to hit to the top, you can chip to the bottom and have a long straight up the hill putt.
Like the achievement name and description, has be putted. Cannot be a chip or hole out from the fairway. Putt. Hence putting perfection.