Welcome to Game Design Breakdown!
Anyways, let's get started.
PATTERNS - GALAGA
One thing you could consider as doing this in an excellent way is Mega Man. I know that Mega Man is a bit of a change of topic, but stick with me here. So, as anyone who's played Mega Man will know, is that all the level design, boss battles, etc. have always been set up in a way for you to... Solve an action puzzle, I guess? Basically, you have to use your skills and brain to find your way around obstacles. Bosses for instance, are all rigged with attack patterns that are completely avoidable, it's just hard to do.
Learning how to avoid enemies is satisfying, and the ability to be able to avoid them, allows the player just enough time to be able to aim and shoot at enemies. Simple gameplay, but endlessly entertaining nonetheless. The player continues to learn, and keeps pushing forward with that knowledge in mind. Just as Mega Man does, it teaches while you play. Learn the pattern to avoid, and you can get around the most intense of situations.
Why not do this? Play the bullet hell game, Squadron to see why. This game differs from normal bullet hell shooters, by focusing on the player's ships and completely scrapping and sense of enemy/bullet patterns. It's not horrible, but certainly not anything special.
Okay, so you probably guessed that I'd start with Galaga. Of course! But what makes Galaga great isn't exactly what makes many others great. You see, there are many different ways to design games. Specifically, there are a few classic formulas for designing action games. One formula is to give the player bad ass weapons, and pit them against a shit ton of enemies. Another, (imo) the best formula, is to create complex patterns that the player must find a way through.
Galaga follows a similar approach, one that is much more followed in older games anyways. (Maybe that's why they're better?) Haha... Yeah, anyways, there's a good ol' pattern set up. I'm sure there's some variation to the enemies movement, still, of course, but the point is, the patterns is what makes the actual gameplay important.
So, why would it be important to focus on pattens in a game? Well, consider games where obstacles are unavoidable. I don't think I need evidence to the fact, that that would suck. Players don't like not being able to avoid/get around obstacles or enemies, unless it comes without a consequence. Even in horror games, you're supposed to avoid the monsters.
Why not fix with stronger weapons/ships? Simply, why "fix" a simple design issue, by making things easier? "Making things easier" shouldn't even be an option in game design.
LEVEL DESIGN - GRADIUS AND AXELAY
like Gradius and Axelay, because they make the player learn how to use their resources most effectively. You remember me mentioning Squadron earlier? I compared it's lack of patterns to a good abundance of patterns. Showing how not having patterns can be a huge issue in a game that should feel like it's covered in them. Squadron, took an interesting approach, not exactly out of the space shooter norm, and oriented the game
To right is a screen cap of Axelay. Those enemies surrounding you must be taken out by a weapon that shoots full 360, called the Round Vulcan. This is an effective creation and use for a weapon system. Not just shooting all over the place at more than random enemies in a more than randomized bullet hell bombardment.
Some great space shooters take a route other than patterns. This route is completely through level design. You remember me mentioning Mega Man earlier? You can think of Galaga, with it's patterns, as Mega Man's boss stages, and Gradius and Axelay, with it's level design, as Mega Man's levels. Level design is crucial for some space shooters,
toward the weapon systems of the ships. Trying to find your way through the obstacles by switching between the ships effectively. I won't comment on it's tedious/annoying control scheme, because that's overkill, but the problem with it is that unlike games that force you to effectively use your weapon systems to the best of you ability to get through the game, Squadron is more than a little bit randomized.
ENEMIES/OBSTACLES - GEKIRINDAN & SHEINRYU
These are two games you may not have heard of, because the two are Japanese games. If you have played them, then you'll know what I mean when I say that they were fucking fantastic! They were both released on Sega Saturn, and are gameplay-wise, relatively the same. They're both more like bullet hell games, barraging you with bullets, but in a nice and easy to follow way, where you rarely get taken by surprise, aside from your own failures.
One thing that really stands out in these games, and I guess that Axelay could come
close as far as the enemies and bullet variations go, but not really filling that level of awesome. These two games are hard AS FUCK! But, they're beyond amazing. There are so many different enemies, so much action, and all of it is pattern based, rigorously, structurally, action packed... AH! They're awesome! If you really want to make a space shooter, play these games on Saturn first, so you have an idea of where to start.
SUMIN' IT UP
So, my last word of advice to you, is that if you're planning to make a space shooter, play these games first. Obviously you can take your own ideas and make them what you want, but if you need to learn the best formulas for the creation of space shooters, taking inspiration from these is a good way to go.