Successfully complete one of the following tasks to get a trophy:

Mexico Complete (Bronze): Complete the Mexico portion of Become a Legend Mode.
Japan Complete (Bronze): Complete the Japan portion of Become a Legend Mode.
Times Square Master (Bronze): Get 1,000,000 points in the Times Square Home Run Pinball venue.
Shibuya Master (Bronze): Get 1,000,000 points in the Shibuya Home Run Pinball venue.
Vegas Master (Bronze): Get 1,000,000 points in the Vegas Home Run Pinball venue.
Retro Times Square Master (Bronze): Get 1,000,000 points in the Retro Times Square Home Run Pinball venue.
10 Times the Fun (Bronze): Win 10 ranked online matches.
Cross-Continental Success (Bronze): Win your first ranked match online.
Power Struggle (Bronze): Win a game on Super Hard in any single player game mode.
Taste of Power (Bronze): Perform your first Legendary Catch in any single player game mode.
Blammo! (Bronze): Fill your Powerup Meter and successfully complete a Big Slam in any single player game mode.
The Slam Dance (Bronze): Strike Out the Potential Home Run Hit on a Big Slam in any single player game mode.
Two for the Price of One (Bronze): Perform a Successful Double Steal in any single player game mode.
Burglar (Bronze): Steal 3 bases in one game in any single player game mode.
Look Out Below! (Bronze): Get 5 Home Runs in a single game in any single player game mode.
Steal Ozzie Smith (Bronze): Win the Ozzie Smith challenge in the Become a Legend Hall of Fame.
Steal Dave Winfield (Bronze): Win the Dave Winfield challenge in the Become a Legend Hall of Fame.
Steal Wade Boggs (Bronze): Win the Wade Boggs challenge in the Become a Legend Hall of Fame.
Steal Reggie Jackson (Bronze): Win the Reggie Jackson challenge in the Become a Legend Hall of Fame.
Steal Ryne Sandberg (Bronze): Win the Ryne Sandberg challenge in the Become a Legend Hall of Fame.
Take that Blimp Down (Bronze): Hit the Blimp with a Big Blast in the Las Vegas Home Run Pinball Venue.
Slay the Giant Brute (Bronze): Hit the Giant Brute with a Big Blast in the Shibuya Home Run Pinball Venue.
Apocalyptic Success (Bronze): Break the globe in the Times Square Home Run Pinball venue .
Happy New Years (Bronze): Hit the New Year's Ball with a Big Blast in the Retro Times Square Home Run Pinball Venue.
Can't Intimidate Me! (Bronze): Get a Wheelhouse Turbo x3 strike vs Legendary Batting Attributes in any single player game mode.
Perfection (Bronze): Get a shutout in a 5 inning game minimum in any single player game mode.
Legendary Strikeout (Bronze): Strike out Babe Ruth.
Against the Odds (Bronze): Get a base hit off of a legendary pitch in any single player game mode.
Double the Fun (Silver): Get 2,000,000 points in any Home Run Pinball venue while playing co-op.
Power Derby Winner (Silver): Come out on top in the BIGS 2 Power Derby in Season mode.
Party Like it's 1881! (Silver): Get a Grand Slam without using the Big Slam powerup in any single player game mode.
Penultimate Perfection (Silver): In a 5 inning (minimum) single player game, prevent the other team from getting an official hit.
Become a Legend (Gold): Complete Become a Legend Mode.
You are the Champions (Gold): Win the World Series and get a season score of 1,000,000 or more at the end of a Season.
Best Season Ever (Gold): Match all of the Legendary Milestones during a season in Season Mode.
Textbook Perfection (Gold): In a 5 inning (minimum) single player game, prevent the other team from getting on base at all.
Hit for the Cycle (Gold): Hit for the cycle in any single player game mode.
Platinum Status (Platinum): Become the greatest of all time.