In this video I complete the entire game without losing a life. This was captured through the super Gameboy adapter on my SNES. Since the first four castles are equally easy I choose to just automatically select whatever one was highlighted at the time. The order I choose to tackle the stages in is as follows with the appropriate links to skip ahead in the video:
Crystal Castle - 0:32
Rock Castle - 6:24
Plant Castle - 12:16
Cloud Castle - 18:52
Dracula's Castle Part 1 - 25:24
Dracula's castle Part 2 - 32:21
Dracula's castle Final Area - 41:35
The only bosses which seemed to be a pain would be the Skeleton Snake which appears at the end of Dracula's Castle part 1 and Solieyu who appears at the end of the second part of his castles. The snake is manageable if you try to stay to the right of the snake and land a couple blows each time he passes through from one hole to another. You can even land blows when the snake is moving through holes slightly off of the scrolling screen to the right which makes it nice. Eventually he always seems to bait me to the left side of the screen, but by this point he is almost dead anyway and falls before I do.
The Solieyu battle is another completely different tactic. You have all the room you need to maneuver but I choose to hold my ground on the right side of the screen and have him to come to me. If you retain the axe for this battle it makes it a lot easier in my opinion. When he hangs out in his left alcove or takes up position on the middle ledge above your position, you can always nail him a couple times with an axe when he pauses to swing his whip or launch daggers. When the fight starts I throw a couple axes at him and then nail him a couple more times while he is on the middle platform. He will begin by jumping over you using the platform above you before he dips down into your trench. When he lands on the right-most platform he will then go under into your area before his return trip. I take this time to leap up to the upper platform using the middle platform as a stepping stone. This give you the chance to nail him in the back as he jumps back over to the left side of the screen. After he passes by, I usually then try to get back into the trench and wait for his next advance, tossing axes in his direction. The second time he loops around the platforms he will go down and then to the top so you will need to reverse your positions to avoid him. He then repeats the same pattern making it easy to land a couple blows and then get out of the way.
When you encounter the final form of Dracula and still have the axe you can land a couple extra blows here and there to make the fight go a little faster, as seen in the video. The trick here is to know where the safe areas are to dodge his rotating projectiles. Once you know this part of it and can determine his predictable pattern of appearances you can land a blow and then retreat to a safe spot.
After this you get the ending and the games credits.