This achievement is awarded for completing the second mission of the game while keeping your flash shot rate over 4.25.
Flash shot rate is the rate at which you kill enemies that enter the screen. The maximum rate is 5.0. If you kill every enemy more or less as quickly as possible you would get a 5.0. This shouldn't be too difficult, I got 4.9/4.8 fairly easily. If you are having trouble though, you can effectively spam bombs, die, spam, repeat.
This difficulty need only be set to EASY. "higher than EASY" is a translation error, it really means "EASY or higher". This can be done in Xbox 360 Mode or Score Attack Mode. Do not turn on DUAL mode.