In order to get the blue scarf, you need to have a pokemon with very high beauty, basicly the maximum in beauty. Then you can talk it to the Pokemon Fan Club Chairman with your high-beauty pokemon in the head position of your party. He will give you the Blue Scarf if it's beauty is high enough.
You can use Sunny Day and Overheat (worked for me), but you might use Bulk Up first. That way you will earn an extra heart each turn (for a total of four + Bulk Ups appeal). Rock Smash is there if you use enough Bulk upps, to score extra points. I'd do this:
Turn 1: Bulk Up
Turn 2: Sunny Day
Turn 3: Overheat
Turn 4: Sunny Day
Turn 5: Overheat