You need to match all of the buttons at the same time as the bouncing ball hits them by pressing the correct button without making a mistake. After each section in the Boss battle, you will have to mash one of the letter buttons on your controller (whichever shows up). If you do make a mistake, just exit and restart the level.
Co-op alone: For doing the boss levels to get the co-op achievement, make sure your second controller is turned on, wait till the last button mash and press on the second controller to join. Then mash the button that is showing on both controllers. If you defeat every boss without making a mistake, the achievement should pop up after you defeat the last boss.