For 6-2, I think it's best to quickly get through those jumps rather than taking your time with them. Figure out how to do them all in one go. It will take some trial and error but you should get the hang of it.
Fortunately the last boss isn't that difficult at all. Sometimes he does a really big jump and you have to connect with a jump kick as soon as he lands. If you're a hair too late you'll get hit. Also try to get him with your three specials. Be careful because he can stun lock you for a lot of damage.