Here is the full list of all 38 The BIGS 2 trophies - there are 28 bronze, 4 silver, 5 gold and 1 platinum.
Become the greatest of all time
Win the World Series® and get a season score of 1,000,000 or more at the end of a Season
Match all of the Legendary Milestones during a season in Season Mode
Come out on top in the BIGS 2 Power Derby in Season mode
Get 1,000,000 points in the Shibuya Home Run Pinball venue
Get 1,000,000 points in the Vegas Home Run Pinball venue
Win a game on Super Hard in any single player game mode
Get 2,000,000 points in any Home Run Pinball venue while playing co-op
Win 10 ranked online matches
Win your first ranked match online
Hit the Blimp with a Big Blast in the Las Vegas Home Run Pinball Venue
Get 1,000,000 points in the Times Square Home Run Pinball venue
Get 1,000,000 points in the Retro Times Square Home Run Pinball venue
In a 5 inning (minimum) single player game, prevent the other team from getting on base at all
In a 5 inning (minimum) single player game, prevent the other team from getting an official hit
Hit the New Year's Ball with a Big Blast in the Retro Times Square Home Run Pinball Venue
Complete Become a Legend Mode
Strike out Babe Ruth
Win the Dave Winfield challenge in the Become a Legend Hall of Fame
Win the Reggie Jackson challenge in the Become a Legend Hall of Fame
Win the Wade Boggs challenge in the Become a Legend Hall of Fame
Win the Ozzie Smith challenge in the Become a Legend Hall of Fame
Win the Ryne Sandberg challenge in the Become a Legend Hall of Fame
Perform a Successful Double Steal in any single player game mode
Complete the Japan portion of Become a Legend Mode
Hit for the cycle in any single player game mode
Complete the Mexico portion of Become a Legend Mode
Get a Grand Slam without using the Big Slam powerup in any single player game mode
Steal 3 bases in one game in any single player game mode
Get 5 Home Runs in a single game in any single player game mode
Get a Wheelhouse Turbo x3 strike vs Legendary Batting Attributes in any single player game mode
Get a shutout in a 5 inning game minimum in any single player game mode
Fill your Powerup Meter and successfully complete a Big Slam in any single player game mode
Hit the Giant Brute with a Big Blast in the Shibuya Home Run Pinball Venue
Break the globe in the Times Square Home Run Pinball venue
Perform your first Legendary Catch in any single player game mode
Get a base hit off of a legendary pitch in any single player game mode
Strike Out the Potential Home Run Hit on a Big Slam in any single player game mode