Fire Bam (ファイヤーバム), released 2/1/1988, developed by Live Planning, released by HAL Labs

This is a “side scrolling action/adventure” type game. The main distinguishing feature is how fast the game is — you move quickly and can often run even faster in some of the areas. The backstory is that the main character (Bam) is about to come of age in the fire clan, but Domez, who fears the Fire Clan’s power, seals away most of the people in other dimensions and turns Bam’s parents into monsters.

The basic idea of the game is that you defeat bosses, which frees townspeople from other dimensions and also increases the available areas you can go in. You can return to the town to buy items from the newly freed people, and to save your game and heal at your parent’s house.

You start with a very basic sword and shield and nothing else, so it’s time to go into the overworld. As I said before, you run very fast. You can swing your sword and jump, but you can also hurt enemies just by running into them in some cases.
If you lose all your lives, you simply return to your parent’s house with no other penalty.

As you beat enemies you get various items, including the “fire” that works as currency to buy things. There are various doors you can enter — some are shops where the people tell you the inventory is sold out, but the instruction manual indicates that you need a special item to have these people sell you things. Other doors take you into separate areas of two types.

One type is a side scrolling area with blowing wind that makes you move even faster than on the overworld. You have to dodge and beat monsters for a while until you come to a boss. The bosses are weird looking; they remind me of that old Godzilla creepypasta.

You can go back in the same door more than once to fight a stronger boss. At some point I assume the door is permanently locked or something like that.
The other thing you can encounter in these doors is one of eight dungeons, which have an obvious inspiration:

These work just like the Zelda II dungeons, and when you beat the boss additional places will open up just like for the windy doors.

The items you can get include swords, shields, boots, and special items. These aren’t just simple stat upgrades, but actually have different effects. Some boots let you jump higher, others make you heavier so you don’t slip. The different weapons have different attack types. One very helpful shield you get early on lets you shoot out projectiles, which was a big help.
Overall this is not a bad game. I think my biggest issue with it is that it’s hard to keep track of where you’ve been and where you still need to go, because the overworld is kind of repetitive and when it increases in size it’s hard to tell which areas are the new ones that have appeared. I had a hard time fighting the bosses but I’ve gotten a lot worse at action games since I was a kid so that’s not surprising.