Richter Strategy:
The Phantom Bat is a large, flying creature that attacks with sonic waves and by swooping down. It's a relatively straightforward fight if you know its patterns. Stay on the ground and whip it when it swoops low. When it flies high, use an upward whip attack or a sub-weapon. The Axe sub-weapon is very effective here, as it can hit the bat even when it's high above. The Cross is also a good choice for consistent damage. Dodge its sonic waves by moving between them or backflipping over them. The bat is quite large, making it an easy target for most sub-weapons.
Maria Strategy:
Maria's Doves are excellent for hitting the Phantom Bat at any height. Her Dragon sub-weapon is also very effective for consistent damage. Use her double jump to easily dodge the sonic waves and to get into position for attacks. The bat is a large target, so Maria can deal significant damage quickly. Her Item Crash will make short work of this boss. Focus on continuous projectile attacks while dodging its predictable patterns.