Obtain the key first
Unlike Feudal Japan, the key and the prisoner of Castle Dracula are not in the same portions of the stage. You'll have to first investigate the lower regions of the castle in order to find the boss that is guarding the key. Once you collect it, you'll need to return to the main floor of the castle, and then ascend to the top where Simon is being held.
Konami Lady's gun
When you walk down the stairs to the lowest portion of the castle, you will see Konami Lady's gun waiting for you in an alcove. However, without the right item, this is purely a trap. It looks like a floating platform can get you down to where the gun is being held. However, this platform will instantly fall away as soon as anybody steps on it, and it's likely to plunge you in the water along with it. You're going to need the Konami Mantle in order to collect the gun. Even once you have it, fitting Konami Man or Konami Lady through the gap while they are flying is tricky. If you're off by even a little, the game will think you intend to land, and your character will fall to the bottom. Trigger the platform to fall, and then carefully maneuver Konami Lady through the gap while flying to reach the gun.
Crossing the water
There's no ferryman in this game. In order to cross over the water and reach the boss at other the end, you'll need to carefully navigate over the broken sections of bridge. During that time, piranhas will jump out of the water to bite you, and Mermen will leap up to the bridge to confront you. Both come so persistently that stopping to attack some of them will only result in more appearing. A couple of the bridge sections contain small hearts, which will make getting across a bit easier. Because the hearts will improve your health, you can effectively ignore the fish and mermen on your first trip, use the limited invincibility you gain from getting hit, and collect the hearts to restore your health.
Use Goemon against the boss
The cyclops frog boss that holds the prison key looks a lot more frightening than he actually is. Despite his large appearance, he is actually quite easy to beat. He follows the pattern of jumping in your character's direction and then landing and spitting a large fireball. If he jumps over your character's head, he will be facing away from the character when he spits the fireball, so you won't have to worry about it. Use Goemon's high attack to your advantage. Let the cyclops frog hop over Goemon's head. Then start hitting it from behind as it blasts fire. Then it will turn around and hop back over to the other side of Goemon and repeat the pattern. If you are standing right in the center, you shouldn't have to move Goemon to avoid taking damage, just duck. Meanwhile, keep turning to face the frog and strike until it is defeated and drops the key that you need to rescue Simon.
After collecting the key, you'll be ready to rescue Simon. Simon is found on the far left side of the hallway that Dracula personally patrols. Dracula's strategy is to warp randomly around the room and attack with a shower of fireballs that fan out. If he appears high off the ground, you won't be able to do much about it, but if he appear low, attempt to knock him out by hitting him frequently and freezing him in place as you did the dragon's in Feudal Japan. Once he is gone, he won't return to bother you until you revisit the castle. There are a couple of interesting features in this hallway. The first is the flashing suit of armor that waits high off the ground. As you might expect, you can't collect this until you obtain the Konami Mantle and gain the ability to fly. The second is a hidden staircase that rises off the highest platform on the right side of the hallway. It will take you to a turret where Simon's special weapon, the cross boomerang, can be seen and obtained. Finally, there is a very helpful warp that will send you back to Dr. Cinnamon's lab so that you don't have to back track all the way. It is found just to the right of the platform with the invisible staircase. Kneel down to activate it.