Make your way through the level normally. After you complete the final bear chase sequence (where you ride the polar bear cub), turn around and jump over the pit. You may need to use a slide-jump to make it. Once across, make your way back through the level until you find the cub. Standing in front of it will activate a secret warp pad, completing the level and depositing the player in the sixth warp room, which is only accessible via these secret exits. Upon exiting the level in this manner, you should unlock the achievement.