Battle Garegga
Assuming you're not a continue-spamming ninny, this is top-tier difficult shooter. The rank system means that you need to be constantly suiciding away your extra lives and teetering one death away from game-over. It also means that you need to score well, or you won't even get the lives you need to suicide. On top of that, the enemy patterns aren't really random, but they're not totally fixed, either, so you need to be very adaptable.
I love it so much.
When the arcade game came out, and later the Saturn port, the developer didn't have any kind of story written up for it - not even a one-paragraph blurb somewhere. There are no characters in the game, no real intro or ending sequences, nothing. Everything depends on the in-game graphics and sound having enough personality to make an impact, and they do. They have a detailed subtlety and colorful grit to them, making Battle Garegga stylistically one of my favorite games ever.
It's also a lot of fun to play. I don't mean to ignore that. But it is going to drive you insane half the time. I often find myself yelling at the TV "I just want to play you, you stupid game!" as I screw up yet another run in one of the first couple of stages.
In the years since, the developer did publish a long backstory for the game...but I don't even want to read it. The game is better without it.