To earn overdrive you must hit a white, glowing section of notes perfectly. Doing this twice will allow you to activate Overdrive. If you have a two player band, both players will need to do this an average of five times each which is possible with Unison Bonuses.
This achievement can be obtained with one person playing Medium Guitar and one person playing Easy Vocals on "Any Man of Mine". Or, if one person has a guitar and microphone, they can do it themselves. To get the achievement, simply play with at LEAST the above two instruments and activate overdrive as soon as the instrument is able.