This is in the menu (bottom screen). In this you can change your signature, see how many badges you have, and see how many stars you have. Now you don't have to do these in order, as long as you get these done. For every your trainer card changes color.
All credit to seribii.net
|(Blue)||Defeat the Elite 4|
|(Green)||Have 5 Shiny Leaves on 1 single pokemon and show it to Lyra/Ethan|
|(Pink)||Set records on all 10 Pokeathlon Events|
|(Silver)||Get a 100 battle-streak in the Battle Tower|
|(Black)||# Complete the National PokÃ©dex. You need to capture all PokÃ©mon other than Mew, Celebi, Jirachi, Deoxys, Phione, Manaphy, Darkrai, Shaymin & Arceus, giving you a total of 484 in your PokÃ©dex.|