For this achievement you will need to surpass the record set by Jack Nicklaus who won the Masters 6 times in his career. This achievement will take 7 seasons of golf in order to achieve, so be prepared for a long slog.
You will want to gain access to the Masters as soon as possible. When you start your career, view the tournament list and hover over the masters to see what you need to complete to become eligible.
Playing at the Masters in this mode is a little different from the other tournaments which you will play in due to the fact that some perks have been turned off. To add a bit of a challenge adding shot power and spin in the air have been disabled. Choosing your shots wisely and having a caddy who is at gold level will help enormously as he will often provide you with a very sensible shot close to the pin. AI scoring is not any different to that of other tournaments as far as i can tell. Highest in the field behind me is usually on 5 under par or thereabouts.
If you are looking to save time there is of course the 1 round tournament option which will enable you to avoid the standard 4 rounds of golf and just play the final day.
Along the way provided you have played and won the tournaments you should unlock the Tiger record achievement of 281 weeks at # 1 which i unlocked just prior to winning the masters for the 7th time.
Good luck beating Jacks amazing record.