Manipulating the game settings is the key to getting every achievement in NHL2k6 easily. These settings can be found after you choose your team in quick play mode. Press the Y button at the settings screen to access them and the bumpers to scroll through the different settings.
For this achievement, set the difficulty to All-Start, set all of the AI skill sliders down to 0 and all of the Human sliders up as far as they will go. It is also best to set the period clock to a full 20 minutes so you have a full one minute to get the goal. It's also best to select a very good team for yourself and a very bad team for your opponent. Denmark seems to be the favorite team to beat up on.
Now, it's simply up to you to score a goal in that first minute. It should be very easy with the sliders adjusted, but if you screw up, just restart and try again. If you want to kill three birds with one stone, get the goal on a fast-break with a defenseman for 3 achievements.
As others have suggested, you can also use a second controller to pull the opponents goalie. This is a surefire way to get the achievement if you have a second controller.