Instructions
Rent a variety of Xbox games with a focus on those with easy-to-unlock achievements. These games are well documented online (see References for links), and include "King Kong," "Tony Hawk: American Wasteland," "TMNT" and "Cars."
Invite a friend to help. For example, if you know someone who played through "King Kong" five times and can't wait for his sixth go-around, invite him to do it while logged into your account, and net yourself an easy 1000 points.
Play online. Some games, like "Far Cry" and "Burnout: Revenge," give out achievement points simply for playing online. In some games, you don't even have to win your online matches.
Download games on Xbox LIVE Arcade. This service offers classic games like "Duke Nukem 3D" and "Doom," so if you spent the 90s playing through these hits, you can breeze through them again to rack up some easy points.