Fear not, those of you who may be worried this is based on percentages, as I thought. I won 20 games as white and got the achievement. I don't believe games won on Beginner count, as I played numerous games and didn't seem to make any progress. However, after a handful of wins against Easy difficulty bots, I got the achievement.
I have a win/loss of 20 - 39, so I'm sure it's safe to say it's not % based. Despite what the 19.84 number implies.