I completed a 1008 piece puzzle in 2 hrs 28 mins.
TwistedFate posted in the forums over on xbox360achievements.org on a very good way to get this achievement. You can find it here: http://www.xbox360achievements.org/forum/showthread.php?t=114569&page=2
I will however copy and paste it here to save you time.
Before you read below, make sure you pick Picture Puzzle, set it to expert, I used the Dream7 picture as it has 1008 pieces but you can use any puzzle as long as its over 1000 pieces, and I picked the last puzzle style, 4th to the right for setting up my puzzle.
Now for TwistedFate's method:
Close the Puzzle Preview window (Hit X until it goes away completely) You won't need to actually see the puzzle for this.
Create 3 piles. Corners, Edges and Middles. Make sure you rotate them at least once so they aren't at slightly off angles. Don't just drop the pieces in a random pile, stack them as neatly as you can on top of each other. It will take a little longer, but you will more than make up for that in a little bit. Also make sure you are near the middle of the screen with your piles so you have some room for the next steps.
Rotate the edges so that all of them have the edge facing the same place. Doesn't matter which direction, you just need them all facing the same way.
When you are done with your piles, grab a corner and set it down on the edge pile. The proper piece will snap onto it. Pick up the new piece and do it again, repeating and adding the other corners until you have the entire border built.
Now zoom all the way out. Then take your completed border and drop it on the inside pieces. Since you are zoomed all the way out the "hot zone" for autosnapping the pieces in is increased so you may pick up more than one piece at a time. (I got up to 7 pieces at at time) Go all around the border adding pieces by picking up and dropping the border on the pile. Once you have gone all the way around, rotate the border and repeat the process. Keep rotating the border every so often and you will have it done in no time.
With the Dream7 puzzle, it took me almost 2 hours to arrange the 3 piles. Make sure to stack the middle pile in the middle of the board. By the time I was done stacking, I had a nice oval going with some pieces that connected when I put them down. So it doesn't have to be perfect but just keep the pile stacking as neat as you can without expanding it too much.
Once I started connecting the middle pieces, I got down to about 24 pieces and just put them in place as it was easy enough to figure it out. I finished the last part up in about 30 minutes.
I put this exact same info over on TA, so you can check it out and give it a thumbs up if you want. Just follow the link: