This achievement is gained by completing all of Bjorn the Unicorns Peggle Institute, they are the first 10 levels of the game. They are more tutorials and are very straightforward.
You will only need to clear every orange peg in a level for this, not the blue ones. You also do not have to worry about optional objectives.
This achievement also only refers to levels, and not the trials, which will earn you a different achievement.
Leftley in the comments below -
"I had that issue of it being stuck at 90% but having completed all 10 levels. It turned out one level (level 9) hadn't recorded a score for whatever reason. After having replayed it the achievement unlocked."