In the Story Mode, along the Path of Go, the first master you meet after your own is the Ferry Lady. She will have 2 puzzles and 4 games for you to play, and when you complete the 4th game she lets you pass to the next master and the achievement pops up.
The games you play are as follows:
1. Finish a partially played game (while being able to use "Suggested Move" and "Undo" for help)
2. Beat the Ferry Lady with a 2 stone handicap (you can no longer use Suggested Move but can still use Undo)
3. Beat the Ferry lady with no handicap as black.
4. Beat the Ferry Lady with no handicap as White.
Overall she isn't too difficult once you understand the basics. With a little trial and error (and maybe help from Suggest a Move and Undo) you can get past her.