A scratch golfer is simply identified as "a player who can play to a Course Handicap of zero on any and all rated golf courses." A course handicap is how many strokes an individual player gets on a specific course based on their handicap index and the course rating. The scorecard par really has nothing to do with defining a golfer's handicap index. A golfer's handicap index takes into account the best 10 scores of a golfer against each course rating, suggesting a golfer's potential average score on a good day.
You can earn a handicap rating after playing 5 rounds in game on handicap rated courses (non match making or private matches).
The easiest way to earn this achievement is by shooting your first 5 rounds in the Korn Ferry or PGA Tour (depending on your starting path) at or under par.