I have decided to work on this game. So far I have done the first level and beat MattyXB's submission by 144 frames. Lag reduction, mostly. I think I can do even better so I will try again and post the first level.
My thoughts are that this will be a take-almost-no-damage and kill-almost-every-enemy run. Why? The game lags badly so killing enemies really speeds things up. Stopping and whipping often saves time! Now the fireball whip can kill small enemies from a distance and bigger enemies fast, reducing lag even more. So in many cases I think the lag reduction from this will outweigh getting hit--definitely through most of the first level. Each level needs to be analyzed separately.
A big timesaver is definitely having at least one powerup on reaching the boss. On the first level it saves quite a bit of time to shoot down the flashing boss summon orb with the fireball, so I think finishing the level fully powered is a must. On the second level it might be fine to have just one orb since you can predict where the next thing will pop out from.
Update: Ok, done with level 1:
http://home.comcast.net/~f_amoroso/CastlevaniaAdventure-TheAxeManv0.4.vbm
Overall about 3 seconds faster than Matty. I take one hit which is about all that's possible for the first level. Most of the time saved is lag reduction. The boss didn't want to behave so I had to wait a bit before picking up his orb. Not sure if there is a better way to manipulate things in this game.