Here is the full list of all 19 R.B.I. Baseball 16 trophies - there are 17 bronze and 2 silver.
Reach base after an AB of 10 or more pitches (vs CPU or Online Ranked only)
Hit 1000 RBIs (any mode)
Win the World Series (Season Mode only)
Qualify for the Postseason in Season Mode (play at least 50% of total games)
Win 20 games within any single month (Season Mode only – sim games don't count)
Score 5 consecutive Wins with your starting pitchers (Season or Postseason Mode)
Score a save in 5 straight games with any pitchers (Season or Postseason Mode)
Win 12 Complete Games in a single Season (starting pitcher must go all 9 innings)
Steal 40 bases with a single player in Season mode
Win an Online Ranked match
Score at least 10 runs and win in an Online Ranked game
Score in every inning of a 9-inning game (vs CPU or Online Ranked only)
Win a 9-inning game without striking out (vs CPU or Online Ranked only)
Hit a Home Run with the Pitcher (vs CPU or Online Ranked only)
Hit 2 consecutive Home runs (vs CPU or Online Ranked only)
Knock out the CPU's pitcher by the 3rd inning
Beat the 2015 HR leader: 48 Home Runs in a season with a single player
Beat the 2015 RBI leader: 131 RBIs in a season with a single player
Beat the 2015 Strikeouts leader: 302 Strikeouts in a season with a single player