How can I unlock those stars? What are the requirements?
According to Bulbapedia, you get a star on your Trainer Card for each of these achievements:
- Get a record in the Hall of Fame
- Complete the National Pokédex (excluding Mew, Celebi, Jirachi, Deoxys, Phione, Manaphy, Darkrai, Shaymin, and Arceus)
- Beat records in all 10 Pokéathlon events
- Show a Pokémon with five Shiny Leaves to Ethan/Lyra
- Defeat 100 Trainers in a row in the Battle Tower