This achievement seems to be a bit buggy. I did it 3 times, doing different methods each time and it wouldn't unlock. So I would HIGHLY recommend you follow this guide exactly that someone posted on ps3trophies.
Start your own GM Connected League. For settings choose 4 min periods, Rookie difficulty, Game period length of 2 weeks, injuries off, Single Game Knockout playoff series length.
Now Choose your team to be Boston or Vancouver as they have the highest overall star rating and should win on their own easier and more consistently than other teams.
Now start simming the 2 week periods at a time and monitor the standings. Make sure you stay in the top 8 for your conference. If you happen to drop to 10th start playing games to get back into the playoff picture.
Once you make the playoffs manually play all 4 games since you can't redo in GM Connected games and win the stanley cup. You can change the sliders in game to favor you and this will not affect the trophy nor will difficulty settings. After winning the cup the trophy will pop once you exit the game. Note you have to actually play the stanley cup clinching game. I simmed it my first time through and didn't get the trophy so make note you HAVE to play the clinching game.
If for some reason you still don't unlock it, back up your user profile on a memory card or usb drive and then delete it from your hard drive and do it all over again.