I really like the concept for the story and what you have so far feels pretty good (Those sound effects are awesome!). The problem is that what you have right now can't really be balanced in any meaningful way. You've combined the procedural generation of Nuclear Throne with the hit-scan (technically in this it's just very fast bullets) combat of Hotline Miami. The issue with that is that Hotline Miami's combat only works because there is plenty of cover and you can learn the level layouts by dying over and over again. In your game, the level generation frequently creates large, empty spaces and the layout changes every time you die. Combine that with the fact that you start over fresh every time and your chances of getting farther than about level 3 are pretty slim. The design is contradictory at almost every level. The way I see it, there are two ways to fix this: change the moment to moment gameplay, or change the overall design. I'll address both of those below:
Make the Bullets Slower:
One option is to make the enemy bullets slower. This is what Nuclear Throne does, and it works very well for them. It would encourage circle strafing and more player movement in general. I would not recommend this, however. Not only would you lose the (fantastic) feature of enemies using the turrets, but it would also fundamentally change the game's identity. Right now, you get the sense that you are fighting against opponents who are largely your equals, as opposed to Nuclear Throne's monsters. There is some actual tension in hiding behind cover and waiting to jump into the fight. It feels like a cross between a Tarantino film with a lot less blood. Plus , the combat is what distinguishes your game from Nuclear Throne, so changing it would really make this game feel like an imitation (right now it just kinda looks like one.).
Scrap Procedural Generation:
I think that the best way to keep the identity of your game intact and also make it playable is to get rid of the procedural generation. As I mentioned earlier, It doesn't really fit well with the other design elements. It's also the weakest link. The caves it generates are, frankly, rather boring. That wouldn't be a problem if it fit in with the rest of the game, but because it doesn't it makes more sense to scrap it than the entire combat system. Aside from the fighting, what really works about your game is the story. It's a clean and simple revenge story that feels as if it jumped right out of a spaghetti western. So designing the game to support it would be a pretty good idea. If it were my game, I would create one, somewhat long, and very difficult level ending with the final boss, who you are taking revenge on. The level would, of course, start out easy and get increasingly difficult, but it would all be planned out to have plenty of cover and relatively small groups of enemies. Players would also be able to learn the layout. The catch is that when you die, you go all the way back to the beginning. As a player gets better, they might learn shortcuts that allow them to skip some of the boring stuff at the beginning.This approach would lend itself to a very tightly crafted revenge story as well as allowing you to take direct control over the pacing and tension, but death would still matter (as it does in a rogue like).
What you have right now is interesting and kinda fun for a few minutes, but you won't be able to make an actual game out of it unless you are willing to make some pretty sizable changes.
