Band streak bonuses are awarded when two or more players in a co-op game get streak bonuses at the same time. You have to get exactly ten in one song for this to unlock. If you have a friend to help you, this should be a breeze; just get the ten bonuses and then stop playing since you can't fail on the game.
If you don't have someone to help you with this, then use the strategy from Perfectionist, but also play either drums or guitar. The vocals will hit everything, so just play along until you get ten streak bonuses, then stop playing. At the end of the song the achievement will unlock.