Radiant Silvergun

First and foremost, you CAN change settings to make this achievement even easier. Choose Single Player > Arcade Mode > Normal Play. Now you will have a few options that you can alter. Change the difficulty to Very Easy, start with 10 ships, and extension every 1,000,000. You can even run out of lives and use continues.

To use the Hyper Sword attack you must fill the bar on the top left of the screen. To do this, you must use your RT sword attack to swipe 10 pink bullets (don't shoot the enemies right away otherwise they may not shoot out these bullets). Also, the end boss of 3A (which is actually the beginning of the game) shoots out a lot of pink bullets so it should not be a problem getting this achievement. When the bar is filled it will now be flashing. When you press RT one more time, you will do your Hyper Sword special attack and the achievement will unlock.