NHL 2K10

Use your right analog stick [RS] to bring up the 2K menu after the loading screen and select "Game Modes" at the bottom.

Select "Season"..."New"....

In the next screen which pops up, make sure the following is set (if I don't list it below, it does not matter what you select):

Season Settings = NHL
AutoSave = Off (so you can reload and try again for the "Red Wings Trophy" achievement)
Season Length = any # you want; I used the minimum of 29
Trade Deadline = Off (simulation goes faster)
Trade Override = Off
Allow CPU Trades = Off
Injuries = Off
Fantasy Draft = None
Customize League = Off
Period Length = 1 minute

Once everything is set, press "Start" to advance...

In the next screen, SELECT ALL 30 TEAMS, then press "Start" to Advance. In the next screen, "NHL Task Automation", I don't think it matters what any of these are, but I set "Lineup Management" and "Simulation Strategy" to "On". Press "Start" to advance again...

At the next screen, "NHL.com", press "Start" on your controller, scroll down and select "Simulate Season". Simulating is real fast, and should take less than a few minutes...

After the regular season is done simulating, you will get a notice that the Playoffs have started. At this point, the achievement for "Blue Jackets Trophy" will pop up!

Continue to simulate through the end of the Stanley Cup Playoffs and if you are lucky, the Red Wings Trophy achievement will also pop.

This solution also works for:

and (maybe):

Edit the rosters of your favorite team to include all the top rated players in the league 85+ rating and up. Start up a Season or Franchise. You can just sim all the games. Half of the teams make the playoffs (top 8 of each conference) so you should get this with no problem. You can also go for the Red Wings (win presidents trophy and cup in same year) and Capitals (win division) trophies at the same time.

Save often in the playoffs and when you get to the cup finals make sure you sweep the series and you will get the Islanders trophy as well.