Completing one of the following tasks adds a single star to your Trainer card, so to have 5 stars you must complete all 5 tasks. Note: Shiny Leaves are obtained by speaking with your Pokemon in certain areas on rare Nature-dependent locations.
Defeat the Elite Four and Champion.
Give Ethan or Lyra five Shiny Leaves.
Break records in ten Pokeathlon events.
Win 100 battles in a row at the Battle Tower.
Complete the National Pokedex (except for Mew, Celebi, Jirachi, Deoxys, Phione, Manaphy, Darkrai, Shaymin, and Arceus).