This Trophy is for completing Story Mode with all 16 original characters that come with the initial release of the game.
It will take you around 2 hours to get this trophy.
Select Story from the main menu and Character Story in the sub-menu. You will be presented with two columns with 8 characters in each.
Each story will take you an average of 5-10 minutes depending on if you skip the dialogue or not. At most there are 4 fights per story with the majority of characters having 3. On the default settings each fight can easily be button mashed through even if you don't know how to play the character.
Here is a breakdown of how many chapters/fights each character has.
Ryu: 4 Chapters, 3 Fights
Chun-Li: 4 Chapters, 3 Fights
Nash: 3 Chapters, 2 Fights
Vega: 4 Chapters, 3 Fights
Karin: 4 Chapters, 3 Fights
Zangief: 3 Chapters, 2 Fights
Rashid: 3 Chapters, 2 Fights
F.A.N.G.: 3 Chapters, 2 Fights
Ken: 4 Chapters, 3 Fights
Cammy: 4 Chapters, 3 Fights
M. Bison: 3 Chapters, 2 Fights
Birdie: 4 Chapters, 3 Fights
R. Mika: 4 Chapters, 3 Fights
Dhalism: 3 Chapters, 2 Fights
Laura: 5 Chapters, 4 Fights
Necalli: 4 Chapters, 3 Fights