Red assassin will keep summoning units until she dies, so focus on her. There are pots for health. I recommend light boots since jump attacks are rather useful against all the sword-based assassins. Try juggling the red assassin to prevent her red combo breaker.
The green assassins primarily do low attacks, so try to stay airborne. If they dash they will do a long combo, so heads up. Try clustering everyone up for Dragon Kicks. Black assassins drop health and die rather easily.