After your Battle Pokemon reach certain Skill Levels, Ribbons will appear on their pictures when you look at the Details in the Menu, your information in My Town, and on their icons in the Character Select Screen.

Ribbon	How to unlock
Bronze Ribbon	After Battle Pokemon reach Skill Level 25.
Gold Ribbon	After Battle Pokemon reach Skill Level 75.
Platinum/Ferrum Ribbon	After Battle Pokemon reach Skill Level 100/MAX.
Silver Ribbon	After Battle Pokemon reach Skill Level 50.