To add onto the above solution:
You must set the CPU Strategy Adjustment to the max setting, otherwise the other team will not pull their goalie in the final minute.
You should simulate the game until your team is on a powerplay or penalty kill. Play a few games to determine if your team takes a lot of penalties, that way you can start on the powerplay. I was drafted by the Flyers, and my team took about 3 penalties a game, so I chose to sim until I got a powerplay. Score on the powerplay and move on.
Teams in this game for some reason do not like to take a lot of penalties, so make sure you turn up aggressiveness for both teams all the way up, as well as the penalty sliders. You can do this DURING THE GAME. This way you can now grab the shorthanded penalty after your team takes a penalty.
Now for the penalty shot, what I liked to do was make sure I put the puck in the defensive zone (your zone) and give the other team possession, then hang around at the blue line. Call for a pass and make sure you are ahead of the defensemen. Hold the A button to puck protect and the computer is more likely to commit a penalty to give you the penalty shot. If you don't get it at first, keep trying, they will eventually trip you. If you still cant seem to get it, try turning up the tuner for poke check effectiveness for the computer - this will increase the amount they make effective poke checks, but for me it seemed like they poke checked more often as well. Don't turn it up all the way otherwise they will strip you of the puck easily.
After you have all these, turn CPU Aggressiveness all the way off. This will make it incredibly easy for you to get your 5 on 5 goal. After that, use the method from the previous guide on how to score on yourself, (by passing the puck into your own net) and build a ONE goal lead.
With about one minute left remaining in the third period, give the other team the puck to bring into your zone. They will eventually pull the goalie (don't worry if it happens late, in my game they pulled the goalie with 28 seconds left), and get the puck. Put it in the net and get the achievement.
If you are missing any of them but manage to get the empty net, you can still get it in overtime, if you manage to tie the game by putting in 2 goals on yourself, which doesn't take that long. This will give you an extra couple of minutes to try and get the one you are missing.
I suggest you use at least 7 minute periods. If you are really struggling with time, 10+ minutes should be more than enough.