Specific to the Lego Star Wars Saga game, I completed the game 100%, and for doing that, you get an achievement, 100 points as Matt said. I didn't get credit for the achievement.
I quit out of the game, shut down the console, then re-started hoping to activate the achievement, but no dice. I called X-Box/Microsoft, they were of no help. Finally, I replayed a random bonus challenge just to see what would happen if I got a new best time. I got a new best time and - Bingo, it triggered the achievement.