Sometimes, the ice tiles are spaced out, and you have to maneuver a lot to be able to touch the ice tiles. The Bunny can make big leaps and control where to land after it, and so can the Lizard. The Student can control where she jumps easily, so she is a better character if you have her.
Contrary to the achievement's description, you can also land on boxes without being disqualified. The only requirement is that you do not land on blue tiles, as alluded to by the name of the achievement.
The name is a reference to the song "Blue" by Eiffel 65.