Here is the full list of all 15 quadrant achievements.
hit more than 9000 beats
unlock the shield in level 3
unlock the star in level 3
unlock the hexagon in level 2
unlock the star in level 2
unlock the pentagon in level 2
unlock the pentagon in level 3
get a streak of 30 in speed training in less than 6 seconds
unlock the hexagon in level 3
unlock the shield in level 2
unlock the star in level 1
unlock the hexagon in level 1
lose for being too soon
unlock the pentagon in level 1
unlock the shield in level 1