Accomplish the indicated achievement to get the corresponding number of Gamerscore points:

The Story Begins (5 points): Clear the first chapter of the Saiyan Saga.
Meeting a Rival (5 points): Clear all chapters of the Saiyan Saga.
The First Z Award (20 points): Clear a chapter with a Z rank on Normal difficulty.
Saiyan Z Award (35 points): Clear all Saiyan Saga chapters with a Z rank on Normal difficulty.
Fierce Warrior (40 points): Clear all of the Saga chapters with the difficulty set to Very Hard.
Full Drama Unlock (5 points): Unlock all of the Drama Pieces for one character.
Saiyan Saga Drama (20 points): Unlock all of the Drama Pieces from the Saiyan Saga.
All Saiyan Fighters (5 points): Unlock all of the Saiyan Saga fighters.
Saiyan Saga Allies (5 points): Unlock all of the Saiyan Saga ally characters.
Worldwide Contender (5 points): Join 10 sessions over Xbox LIVE.
Worldwide Warrior (5 points): Create 10 sessions over Xbox LIVE.
Battler (Default) (5 points): Play the Survival Trial (Default Drama).
Speed Beyond Terror (5 points): Clear the Time Attack Trial (Course A) and get a result.
Score Beyond Terror (5 points): Clear the Battle Point Trial (Course A) and get a result.
A Beginner Awakens! (5 points): Clear Basic tutorials.
Bloodless Victory! (20 points): Win a battle without taking any damage. (Z Chronicles/Versus only).
Destructive Win! (5 points): Win a battle while changing or destroying the background. (Z Chronicles/Versus only).
Unleashed Ki Win! (5 points): Transform, use Aura Spark, and win with an Ultimate Attack. (Z Chronicles/Versus only).

Additionally, there are 32 secret achievements:

Advanced Victory! (15 points): Clear Advanced tutorials.
Legendary Warrior (15 points): Clear all chapters of the Frieza Saga.
Ultimate Warrior (15 points): Unlock all characters' Ultimate Attacks.
Survivor (Default) (35 points): Play the Survival Trial (Default Drama) and defeat 50 opponents.
Survivor (Custom) (35 points): Play the Survival Trial (Custom Drama) and defeat 50 opponents.
Frieza Z Award (35 points): Clear all Frieza Saga chapters with a Z rank on Normal difficulty.
Z Warrior (40 points): Clear all of the Saga chapters with the difficulty set to Z.
Birth of a Legend (100 points): Play the Survival Trial (Default Drama) and defeat all opponents.
Goku's Father (20 points): Unlock Bardock.
Legendary Saiyan (20 points): Unlock Broly.
All Drama Pieces (40 points): Unlock all of the Drama Pieces for all characters.
Intermediate Fire! (5 points): Clear Intermediate tutorials.
Ultimate Unlock (5 points): Unlock all of one character's Ultimate Attacks.
Sturdy Warrior (20 points): Unlock all fighters.
Frieza Saga Drama (20 points): Unlock all of the Drama Pieces from the Frieza Saga.
Cell Saga Drama (20 points): Unlock all of the Drama Pieces from the Cell Saga.
All Frieza Fighters (5 points): Unlock all of the Frieza Saga fighters.
Frieza Saga Allies (5 points): Unlock all of the Frieza Saga ally characters.
Master of History (15 points): Clear all chapters.
All Cell Fighters (5 points): Unlock all of the Cell Saga fighters.
Family Bonds (15 points): Clear all chapters of the Cell Saga.
Cell Saga Allies (5 points): Unlock all of the Cell Saga ally characters.
Cell Z Award (35 points): Clear all Cell Saga chapters with a Z rank on Normal difficulty.
Z Master Award (35 points): Clear all chapters with a Z rank on Normal difficulty.
Ultimate Z Fighter (100 points): Clear all of the Saga chapters at difficulty Z, with Z ranks.
Ultimate Survivor (100 points): Play the Survival Trial (Custom Drama) and defeat all opponents.
Battler (Custom) (5 points): Play the Survival Trial (Custom Drama).
Speed Beyond Power (5 points): Clear the Time Attack Trial (Course B) and get a result.
Speed Beyond Rivals (5 points): Clear the Time Attack Trial (Course C) and get a result.
Score Beyond Power (5 points): Clear the Battle Point Trial (Course B) and get a result.
Score Beyond Rivals (5 points): Clear the Battle Point Trial (Course C) and get a result.
Powerful Allies (15 points): Unlock all ally characters.