Yup, the air-combo is the key in most bosses... Just wait til the mini-monsters appear, kill them quickly, and when your sword is flashing pink go for the boss, never before that...
I'm on stage 8-B, I absolutely hate dying because of a bad jump and having to restart all over again....
I agree the sword-dogs are incredible difficult, but when I was playing that stage I still hadn't learned to use the anti-blocking kick (the problem of the dogs is that they are always blocking...) and hadn't understand how to charge the sword by quickly killing enemies (although I always tried to kill them quickly just to watch the tate, so I was using it anyway...).
This game just buttrock !