If you are looking to get this achievement with your favourite team, I strongly recommend utilizing the direct sim feature on each game day. This takes you to a secondary screen, and simulated the game by the following:
End of first period
End of Second period
Five minutes left in third
End of game
If you watch the right side of the screen, there is an intervene bonus that only goes up when you're about to start losing. If you see it start to go up heading into the third, sim and get the win (takes about 5 minutes per game) and you'll be well on your way to winning the league. It's awesome because you don't have to play the games that are guaranteed wins.