So, 
The premise of the game is that you are playing as Dr. Jekyll, who created a potion to divide the good and evil of the human psyche and tested it on himself. This caused his evil persona Mr. Hyde to be born. The game takes place on Dr. Jekyll's wedding day, and the goal is to get him to the chapel so he can get married.
The title screen shows Dr. Jekyll looking at his test tubes... I kept waiting and waiting for it to show him drinking one and transforming into Hyde, but it never happened. We just have to press Start.
The game actually has two separate "modes" representing the good and evil of the psyche. When you're playing as Dr. Jekyll, your main goal is to go on a walk to the church. But your walk is not a pleasant one, along the way, you encounter many "stressors" that will "frustrate" Jekyll, and when he gets too upset, the alter ego Hyde awakens!
The only thing you can do as Jekyll is walk, hop, and swing your cane in front of you, hoping to avoid stressors and continue walking to the right to make it to church.
The cane sounds like it could be a cool "attack," but it seems to do literally nothing except in two cases: one, it can swat bees (which is actually pretty cool, if you can land it), and two, you can poke the singing lady and it will instantly kill you for... whatever reason.
Jekyll seems to be easily-stressed, as he flips out at things such as barking dogs, playing children (granted they do shoot him with a slingshot), singing women, and people walking a little too fast.
Some of his stress is more understandable, such as birds pooping on him or getting harassed by swarms of bees. Or a man in a pink tuxedo dropping explosives on the ground that literally blow Jekyll up. You know, like you normally encounter on a walk to church.
Stress Jekyll out too much, and Mr Hyde awakens. Unlike Jekyll, whose goal is to walk to the right, Hyde walks to the left! In fact, he automatically walks to the left (whereas with Jekyll you can just stand in one place if you wanted to), constantly approaching Jekyll's location in a warped version of the world.
If Jekyll and Hyde ever meet, a lightning bolt strikes them down and they are dead forever. And you have to start over. So you really want to make sure Jekyll progresses more to the right than Hyde progresses to the left.
To stop Hyde from moving left, you need to fight off demons that are attacking him. I didn't read the manual well enough before my first play, and literally thought you had to punch the enemies. Because Hyde has a punch attack. The punch attack does nothing. I have no idea why it even exists.
But if you hold the up button and press the punch button, Hyde will use his PSYCHO-WAVE! This shoots a little ball around the screen in an incredibly stupid wave pattern that makes it really difficult to aim. It certainly won't hit things directly in front of you, so you have to memorize its strange trajectory and try to pinpoint when enemies are in its way, then time shooting it... it's a blast, let me tell you.
As Hyde defeats demons with his Psycho-Wave, the sanity meter slowly replenishes and eventually he'll turn back into Jekyll, and you can start walking to church again.
Another "fun" thing about this game is that you have a life meter, and it depletes as both Jekyll and Hyde. Getting blown up by a bomb will deplete a ton of this, to the point where it's really common that you turn into Hyde and then immediately die because you have no life. And the only way to regain life is to finish a Hyde session and return to Jekyll. So basically if you hit a bomb you're screwed and going to have to start over.
I eventually got to a point of the game where barrels were rolling out constantly from the side of the screen, and every time a Bomb Maniac left and exploded his bomb, another Bomb Maniac appeared. I basically was walking a few steps, purposely hitting barrels and avoiding bombs to stress out Jekyll so he'd turn to Hyde, then have him turn back to Jekyll again, which makes no enemies appear for a short time. Like, half a screen. And I was doing this over and over...
I eventually got so frustrated I stopped playing and went on to do my review of Mega Man, after not playing for a full day.
I decided to look up a guide on GameFAQs and learned quite a bit about the game!
The most important thing I learned was that I was on the final stage of the game. But interestingly, there are actually two endings to the game! To get the "normal" ending, you just walk Jekyll to church without Hyde ever catching up, and you win. To get the "good" ending (which to me is more a "true" ending than a "good" ending), you have to get Jekyll to the Street stage (stage 6, the final stage), then let Hyde catch up to the Street stage. Hyde will instead climb on the rooftops, which allows him to "pass over" Dr Jekyll, so that they never actually meet and no lightning kills them. This summons a boss fight where Hyde fights the ultimate demon or something and then you return to Jekyll. Now there are no more stressors and you can just walk to the end of the game! Very exciting walking gameplay.
When you reach the church, Dr Jekyll and Ms Millicent get married, like in the "normal" ending... but then a lightning bolt crashes down on the "END" screen and the word "END" goes backward, with a silhouette of Hyde holding a cross in the background. Spooky ending!
To be honest, I would have ended up getting this ending anyway with the way I was playing. In fact, I think getting the "normal" ending is probably harder, as you have to avoid all those barrels and bombs and actually beat the sixth level.
But what was more interesting is that I learned that this game's Japanese release actually had more content! In Japan, the game was also released by Bandai under the title ジーキル博士の彷魔が刻, Professor Jekyll's Demon Time, which contained two unique levels (the English version just copy/pasted two other levels over them so you literally go through those same two levels twice) and unique enemies! All of the enemies are listed in the English instruction manual, but only some of them appear in the game.
In fact, the English manual says that there are certain points in the game where you can earn coins while playing as Jekyll, but that also was removed from the English version, making the English manual... less than reliable with all of its misinformation. My guess is that they just directly translated the Japanese manual without caring to note the changes made to the English version of the game.
Nothing was offensive or obscene or anything, so it's not like it was a censorship issue. They just... decided to cut a bunch of stuff from the game?
So I tried playing the Japanese version of the game to see how different it was. It was definitely a more interesting experience with more characters and locations, but the game was still the same thing. Walk to the right and get "stressed" by a constant onslaught of increasingly difficult hazards, and then walk left and fire a Psycho-Wave and pray that it hits your enemies.
In all, I didn't actually hate the game, and if I was a kid playing this, I might have even have developed a fondness for it, as I did with other bad games when they were the only thing I had to play as a kid.
The concept of the "good versus evil" being two separate sets of levels that eventually "clash" if you let the bad levels play on too long is quite interesting, and having the main gameplay be walking down the street to church was certainly unlike other games.
It's at least a unique experience, and if you're a retro game buff, try loading it up in your favorite emulator (I recommend playing the Japanese version!) or finding a copy of the game if you like collecting. It's definitely not a "so bad it's good" game as it's not that bad, but I'd hesitate to call it an outright bad game. The interesting concept behind the game is enough to make me appreciate it, I guess.
Thanks again