An explanation of the strategy for the Archangel Catsiel boss fight.
Catsiel will sometimes whip its tail at you, so stay at the bottom of the screen and keep moving. If Catsiel winks, it's about to jump into the air, and if you are on the ground when it lands, you will be injured and stunned, so be sure to jump before Catsiel lands, and don't be in front of it when it lands. After it lands, Catsiel will display a wavy line on its screen just before shooting the screen at you. When its real face is visible, it's vulnerable, so attack it then.
If Catsiel is the boss of the fourth dungeon or later, there will be a second phase of the battle. In the second phase, Catsiel's screen will show arrows. A joystick will appear on the ground. Hit it with your sword so that the joystick moves in the direction indicated by the arrow on Catsiel's screen. There will also be enemies to avoid during this phase. Once you have input the correct sequence using the joysticks, Catsiel will be defeated.