To get this, just play "In Da Club" by 50 Cent with the appropriate character on their birthday. You can choose your character in Perform mode after selecting the song difficulty.
When playing on a character's birthday, check out the level-up counter in the top-right corner after playing a song. If it's your character's birthday you will get bonus stars and a notification ("Rasa's Birthday"), even during story mode.
If you can't wait for one of these dates to roll around, you change your system date to get this offline with one of the dates below. Characters that must be unlocked via leveling up are marked with an asterisk (*).
Credit to samqwe for grabbing the PDF with all birthdays off of Harmonix's site.
Characters - Birthday
Emilia: February 3
Angel: February 14
* Dare: February 28
Taye: March 9
* Frenchy: April 13
* Marcos: April 18
* Jaryn & Kerith: June 4
* Cyph-56 & Cyph-78: June 11
* Kichi: July 24
* MacCoy: August 24
* Shinju: September 2
Rasa: October 16
Miss Aubrey: October 20
Lil' T: October 30
Mo: November 11
Bodie: November 23
Glitch: November 26
Lima: December 9
* Oblio: December 25
* Dr. Tan: December 31