In the case of this achievement, you get this while you play through the story
For getting the Highest Honor for a Avatar, you need to gather points for all races:
-Dog
-Wolf
-Cat
-Rabbit
-Hedgehog
-Bird
-Bear
You get medals after earning a certain amount of points, keep playing until you get 3 Gold Medals with an avatar species, once you get it, choose a new avatar and do it all again
As for a Stage recommendation, i used Secret Stage 6: Reverse Block 1