Yeah since its based on averages, you definately want to get it from the first game. Also make sure if you dont get it on your first try exit from your be a pro without saving saving and then reload your profile, do not save your profile after a game with bad stats or you will have those bad stats bringing your average down.
Also found a VERY easy way to do these.
1. Start with clean profile sim games to 5 min mark of third and get all A's. (If you dont get all A's then exit season without saving and reload profile so it doesnt keep the previous games stats.)
2. Play the next game fully, dont need stats in this game just need a full game for achievment to unlock at the end of.
Just sim the game an intervene in the 3rd period to play the last five mintues. I found when only palying these five minutes you will most likely get A range for Position and Teampaly grades - apparently its such a short amount of time they don't expect much from you. The only thing that requires any sort of skill/effort on your part is getting the Stats to be in the A range.
For a goalie you just need a few saves, and im sure winning the game and shutout will help too (it was 3-2 for my team when I intervened, made a couple easy saves and that was enough for me).
For center/defense/winger you just need to get a point (goal or assist) and youll be golden for Stats. So you can keep resimming/loading till you manage to get one, or even easier, just keep simming till you get a score where your team is ahead by 1 or 2 goals. This will ensure the other team will pull thier goalie (usually around the 1:00 min mark). Obviously an empty net makes it much easier to get a point. So try to get possesion and score yourself or assist on a goal.
(When I got this for D and W, I was completely ignoring the postition arrow trying to steal the puck from the other team till I got the puck and put it in the empty net. Still got an A for Position so really jsut do whatever you need to to score.)
Doing this will earn you the achievement. However, it doesnt unlock at the end of the game, because it wasnt a full one it seems. To get it to unlock just play the next game of the season. You don't even have to touch the controller jsut let the game run out and it recognizes you met the requirement from the last game and the achievement will pop up.
For those curious I did all mine in NHL pro seasons, chose good teams and good palyers - Crosby, Fluery, D. Seden, S. Neidermayer. It was jsut easier for simming and scoring with a good palyer/ good teamates.
Anyways these achievements can be done very easily with minimal skill this way. Just have to make sure you set thing up the right way.
Hope that helps people