The requirement of getting all the levels of an island with three stars can be obtained on any island, however... Island A is (by far) the easiest to do this.
All you have to do is complete each of the 10 levels on the Island (Island A for example) with 3 stars. This is done by completing a level without dying.
The first level which you complete with 3 stars (presumably level A1) also rewards you with the "Professor" achievement.
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