As no one has posted a guide for this I thought I would give my opinion on the best way to crack this achievement.
Firstly the way this achievement is set up is different to last year's game. 2012 asked you to achieve so many Birdies, Eagles, GIRs etc in a single round to get Gold whereas this year you just have to get a collective amount over as many rounds as you like. There are pros and cons to this and I think some of the more skilled players will prefer last year's approach as effectively you could get Gold in 3 good rounds (You had to get Bronze and Silver before you could get Gold hence the 3 rounds). This year any progress you make towards Bronze or Silver will count towards the Gold level but the targets are higher meaning more rounds are needed. There is no doubt that this year's approach opens the door for lesser skilled players to obtain this achievement by simply replaying the same course multiple times until they achieve the target requirements but this might get boring real quick.
To get a Gold Mastery level on a course you need to complete the following objectives:
6 Under Par Round
Hazard Free Round (Reduced Wind Pin helps with this)
60 Career FIRs
80 Career GIRs
20 Career One Putts
100 Career Pars or Better
30 Career Birdie or Better
5 Career Eagles or Better
This means that if you have 6 good rounds on a single course you should get the Gold Mastery Level. I have found that the "Y" button is your best friend in this situation allowing you to skip any cut scenes after you have hit your shot. If you wanted to make things even easier play the game on Amateur and enable auto caddie so the default shot you get should always be on/near the target meaning you can just swing, press Y and sing again until you finish the hole. This speed golf approach should see you completing a round in under 20 minutes. For those of you actually wanting to play the game normally I found that using some of the boost pins helps to aid the speed of your round. I have been using the pin that calms the wind (gold level) meaning I'm not spending time factoring in huge gusts when I'm lining up my shot resulting in quicker round times. I have found that any Accuracy pins result in shots been closer to the target (Ironic I know) hence time is not wasted trying to read multiple breaks on long putts. This method has found me completing a round in about 30mins. From what I have scene you can gain progress towards course mastery levels in any game modes (even though it says Career). I have been gaining most of my progress in the Main PGA career mode but I already had some from completing the Tiger Legacy Challenge Mode and playing some games online (through the country club menu). This means that if you are getting bored of grinding away you can swap and change modes to keep things interesting.
You can keep track of your current progress from the Main Menu -> Game Modes -> Course Mastery
So in short
Use Y to skip cut scenes after shots
Use Boost Pins to reduce wind and improve accuracy
Use Auto Caddie to set up shots for quick execution
Mix and match game modes to keep things interesting
If anyone has anything to add to this guide then please comment below.
Just a quick update to this guide since I gained the achievement.
I was mostly playing the main career mode "Road To the PGA Tour" as i was going for the 7 green jackets achievement. I found that tournaments that are on courses that you don't have (ie DLC) allow you to change the course to one of your choosing. This was a nice helping hand along the way as I was only playing a few tournaments a year to stay in the Top 100 EA rankings to qualify for the Masters. After getting the Green Jacket achievement I switched to the "Play Now" game mode (using my created character) and just played stroke play with the course wind conditions set to calm. The Augusta Par 3 course was the easiest to master and only took me about 5 rounds to get gold. All in All this achievement took me about 3 days to crack so be prepared for a long haul. I tried watching a DVD or listening to music at the same time to help cure the boredom .