For all of the "Fever" achievements, simply play three songs in a row in the listed genre. The genre is listed at the top of the screen as you select songs, which should make this easy. In fact, you can play a single song, retry it twice and it'll still count towards the achievement.
I don't know if failure counts as a "play," but otherwise score doesn't matter. I did it on Light difficulty -- as long as you stay with the earlier songs it's hard to fail.