You'll need to play 21 rounds in total. Use the following settings for the tournaments to do this the shortest way - Quick Play/Quick Tournaments/pick the major you're competing in - Change the scenario to 'Solo Leader' and change any course settings to your preference.
You will need to play each major enough times to become the all time win leader for each, as below:
The Masters Tournament - 6 wins
The Open Championship - 6 wins
US Open Championship - 4 wins
PGA Championship - 5 wins
You can check your progress by setting up in the way mentioned above and when prompted to select an event checking the all time win leaders list for any of the majors.