Bronze:

Mexico Complete
Complete the Mexico portion of Become a Legend Mode    

Japan Complete
Complete the Japan portion of Become a Legend Mode    

Times Square Master
Get 1,000,000 points in the Times Square Home Run Pinball venue     
    
Shibuya Master
Get 1,000,000 points in the Shibuya Home Run Pinball venue    

Vegas Master
Get 1,000,000 points in the Vegas Home Run Pinball venue    

Retro Times Square Master
Get 1,000,000 points in the Retro Times Square Home Run Pinball venue

10 Times the Fun
Win 10 ranked online matches

Cross-Continental Success
Win your first ranked match online     

Power Struggle
Win a game on Super Hard in any single player game mode     

Taste of Power
Perform your first Legendary Catch in any single player game mode     

Blammo!
Fill your Powerup Meter and successfully complete a Big Slam in any single player game mode    

The Slam Dance
Strike Out the Potential Home Run Hit on a Big Slam in any single player game mode     

Two for the Price of One
Perform a Successful Double Steal in any single player game mode     

Burglar
Steal 3 bases in one game in any single player game mode     

Look Out Below!
Get 5 Home Runs in a single game in any single player game mode

Steal Ozzie Smith
Win the Ozzie Smith challenge in the Become a Legend Hall of Fame     

Steal Dave Winfield
Win the Dave Winfield challenge in the Become a Legend Hall of Fame     

Steal Wade Boggs
Win the Wade Boggs challenge in the Become a Legend Hall of Fame     

Steal Reggie Jackson
Win the Reggie Jackson challenge in the Become a Legend Hall of Fame     

Steal Ryne Sandberg
Win the Ryne Sandberg challenge in the Become a Legend Hall of Fame     

Take that Blimp Down
Hit the Blimp with a Big Blast in the Las Vegas Home Run Pinball Venue     

Slay the Giant Brute
Hit the Giant Brute with a Big Blast in the Shibuya Home Run Pinball Venue     

Apocalyptic Success
Break the globe in the Times Square Home Run Pinball venue     

Happy New Years
Hit the New Year's Ball with a Big Blast in the Retro Times Square Home Run Pinball Venue    

Can't Intimidate Me!
Get a Wheelhouse Turbo x3 strike vs Legendary Batting Attributes in any single player game mode    

Perfection
Get a shutout in a 5 inning game minimum in any single player game mode     

Legendary Strikeout
Strike out Babe Ruth     

Against the Odds
Get a base hit off of a legendary pitch in any single player game mode    

Silver:

Double the Fun
Get 2,000,000 points in any Home Run Pinball venue while playing co-op

Power Derby Winner
Come out on top in the BIGS 2 Power Derby in Season mode

Party Like it's 1881!
Get a Grand Slam without using the Big Slam powerup in any single player game mode

Penultimate Perfection
In a 5 inning (minimum) single player game, prevent the other team from getting an official hit

Gold:

Become a Legend
Complete Become a Legend Mode

 You are the Champions
Win the World Series® and get a season score of 1,000,000 or more at the end of a Season

 Best Season Ever
Match all of the Legendary Milestones during a season in Season Mode

Textbook Perfection
In a 5 inning (minimum) single player game, prevent the other team from getting on base at all    

Hit for the Cycle
Hit for the cycle in any single player game mode

Platinum:

Platinum Status
Become the greatest of all time