I did these online and the only way I could get these to count was with mercy wins as the home team. Mercy wins on the road and regular full 9 inning game wins at home or on the road did not move the tracker for me. A Mercy win requires you to have a 10 run lead. If you are the home team, you will win the game as soon as you get the 10 run lead. If you have two Xboxes you can easily boost this by playing against a dummy account. Otherwise boosting with a friend will work. I did not try playing against the CPU but it is in the description so that should work as well, it will just take longer.
An example of one team to beat from each division is:
Tampa Bay Rays - AL East
Detroit Tigers - AL Central
Texas Rangers - AL West
Miami Marlins - NL East
Cincinnati Reds - NL Central
San Diego Padres - NL West
Check the tracker after each win to make sure it counted and if not you may have to try that division again. This game is buggy on achievement tracking like every year.