"Stacked Achievements" refers to the achievements system on the xbox 360. All 360 games have certain goals or challenges that when performed earn achievements. Each achievement adds to your gamerscore. A stacked achievement works like this: Say you have 8 chapters in a game and each chapter beaten earns a 10 point achievement. Chapter 1 beaten on easy would be 10 points, 20 points on medium, and 30 points on hard. If you beat Chapter 1 on hard your first time playing, you would unlock all 3 achievements for easy medium and hard. This would be a total of 60 points, and is called "stacked" because you earn all 3 without having to play through Chapter 1 3 times, once on each difficulty. Not all 360 games offer stacked Achievements, you can search the internet for games that do. Some examples include Gears of War and Halo 3.
"I beat Halo 3 on Legendary (very hard) my first time playing and got all the stacked achievements."