When in the Options menu, if you click on He Runs, Japonesque, Shinobi Walk, Sakura, and Getufu (in that order), you will be completely invincible. You can complete the level without taking any damage at all and still earn the achievement. You can also go into options, set level to easy and shurikins to 70. Then complete the first level. Just keep heading right and attacking anything that moves.
Against the boss, he will leave himself open for a split second before attacking, so shoot him then. After, head away from him and jump back over him as he dashes across the screen. Rinse and repeat.