This achievement is similar to "Chiggedy Check It Out," but just requires that you play Streak in Battle mode. You can accomplish this online or offline if you just win 6 mixes. by a streak of 20. You can however pick a list with 6 songs and nail it down in one run.
(Streak mode is played by racking up a note streak and pressing the Euphoria button to bank it. Once banked, your streak resets and your posted streak will remain until you bank a higher one.)
Other than Chiggedy Check It Out" you can't do this alone in the Empire Mode.You need to do this either offline with two Turntables or online with a boosting friend.