Here is the plot for Legendary Wings, according to Wikipedia:
Legendary Wings is set in a distant future where an alien supercomputer named "Dark", which has been helping human civilization achieve a new state of enlightenment since ancient times, has suddenly rebelled against mankind. Two young warriors are given the Wings of Love and Courage by the God of War Ares in order to destroy Dark and ensure mankind's survival.
Level 1
The Control Pad moves, A shoots and B shoots bombs.
The first sets of enemies move around in a circle but will eventually charge at you, so take them all down. After this, a flashing circle will fly around. Shoot it and grab the P icon to change your single laser to a double laser. This makes your weapon more powerful, and if you get hit, you'll go back to the single laser before one more hit kills you. The more you power up your weapon, the more power levels of weapon you can lose to the enemy and the more hits you can take.
The gray turrets that shoot at you can only be destroyed with bombs. By taking them down, you can make flying around and destroying enemies a little easier.
The enemies with the pink brackets for wings will slowly fly forward and slowly move to the side towards you, but they can be easily taken down.
The Level 3 weapon is an energy wave that travels all the way to the top of the screen.
The big face in the ground will open its mouth and shoot whirlwinds at you. If the whirlwinds get you, you'll be sucked into the mouth and you'll have to fight enemies to get back out, but the whirlwinds here are pretty easy to avoid.
The enemies that look like shells take a lot of hits to destroy, but they can be destroyed.
The flying statue heads are indestructible. When you see them, hang all the way back and fly around them to avoid getting hit by them.
The blue balls will turn to enemies that shoot at you before charging to the bottom, and the ships that show up afterwards after that will fly to the bottom, shoot at you, then go all the way back up. Shoot as many of those enemies down as you can without getting hit.
After this, one of the turrets will create a whirlwind when bombed. This time, let the whirlwind touch you. You'll be carried into an underground bonus area where you can collect King Tut heads and snake statues for a ton of points. Here, you'll be in the horizontal shmup mode in a game where most of the action is of the vertical shmup variety. While you can't drop bombs, you can still move and shoot. Shoot down the walls if you're about to get trapped; you'll find a hole in the wall to travel through somewhere. Also, if you see something inside of a wall; shoot it. You'll be able to find P icons and hearts that give you continues in these secret underground areas.
The Level 4 weapon is a fireball with two smaller fireballs that move up and down following it, while the Level 5 weapon is the "Turtle Dove" form, also known as the "Psycho Flame" weapon in the arcade game. The Psycho Flame does the most damage to enemies and wastes the majority of them in one shot; unlike the arcade game, however, the most powerful weapon also gives you two extra hits before your weapon goes back down to Level 4 upon taking damage. Picking up P icons allows you to restore those extra hits.
Watch out for the enemies near the statues that you can't pass through, and stay near the bottom for the spinning enemies, so you don't get shot.
When you see the statues with the wings; bomb the faces and avoid the projectiles. At the end, take out the statue head, then shoot at the dragon that flies around while avoiding its attacks. When the dragon heads back to the center, hang all the way back and get to the center, then shoot at the dragon as it gets close to - but never reaches - the bottom of the screen. Once you beat the dragon, you can enter the temple.
Inside the temple, destroy the pink panels in the background wall when they flip around and reveal their turrets. As for the blue machines that fire lasers downwards on the ceiling, avoid the attack before attacking yourself. For the green enemies that hang on the floors and ceilings, wait for their attack, then attack them as they move.
The boss here has an opening in the center that you can shoot at while moving around the projectiles that they shoot, but you also want to shoot down the eyes on the side of the boss as they are open without getting shot by them yourself.
Once you beat this level, it's on to the second of five levels in the game.
Level 2
The enemies at the start are much like the enemies from Level 1 that slowly turn towards you. The flying eyes move towards the bottom of the screen in a sine wave pattern. You'll then have some slow moving enemies moving towards the bottom of the screen as well as "claw" enemies that move towards the bottom, shoot, then retreat.
The turrets are back, but they're actually in every stage.
The gray shells after the giant face fire at you if left on-screen long enough. The light blue enemies fly around in a circle before flying to the bottom.
After the two sets of light blue enemies, there is a turret that takes you to another bonus area. This one looks exactly identical to the bonus area in the first level, but there will be more continues and P icons hidden in the walls.
After some more enemies, you'll see the projectile-spitting statues, which are all in the same locations as before (and always will be). The dragon fight goes the same way as Level 1 (and always will be, too).
In the temple, shoot your way through the columns, then avoid the quicksand while taking care of the enemies. Once you're in an open area, shoot down all of the blue bugs that fly towards you to avoid taking damage. Stay on the top route afterwards to avoid enemies.
The boss is the same as before, but there are four eyes on the side as opposed to three. Despite this, the end of level boss is the same as ever.
Level 3
At this point in the game, there will be walls that you can't shoot or fly through, which makes navigation - and avoiding some enemies - harder. There will also be turrets that follow you around and aim at you in certain directions, and you'll need to take care of them whenever possible.
The gray mine balls will shoot an eight-way spike shot, but if you concentrate a lot of firepower on them, they will go down easily. Also, the gray crescent enemies will shoot spikes diagonally downward. Take out as many as you can. There will also be mine-dropping enemies that go down super easily as long as you keep firing, especially on the higher weapon power levels.
One of the ground turrets out in the open will take you to a hidden bonus area. You'll definitely want to go into it; it'll give you a breather from the vertical shooting action.
The enemies that fly downwards in a sine wave pattern in pairs shoot shrapnel at you if you destroy them; if you leave them be, the shrapnel travels upwards instead.
After the temple entrance (which is the same as ever), you'll want to wait for the ceiling turrets to fire before passing by them. From there, be ready to fire at walls and take out enemies carefully.
The pink robots that assemble themselves and come at you will shoot a fire shot if they get too close, so shoot them down as quickly as possible.
The boss here has five eyeballs. If you can't fire at the boss, work on the eyes and avoid the eyeball shots to make things easier on yourself.
Level 4
The spikes on the green walls hurt. Don't touch them. Also, the gray "X" shaped enemies are indestructible even in your Turtle Dove form, so you're better off avoiding them.
The drill enemies will charge at you from the side if you line yourself up with them. If they look the least bit familiar, that's because these drill enemies showed up in Dr. Wily's Castle in Mega Man 2.
There are foreground elements that you can fly through, and these elements can make it harder to see some enemies coming at you. Keep an eye out for enemies and be ready to avoid things, especially in these narrow corridors.
After the temple entrance, let the green enemies that fire to the sides come to you, and fire at them as they move. Be ready to blast walls and grab P icons in case you've taken hits in Turtle Dove form or if you need to power your weapon up, as this is the only level that I could not find a bonus area in.
The boss here has seven eyes. You'll definitely want to take a few eyes out before finishing the boss off.
Level 5
Take out as many ground turrets as you can to make fighting off enemies easier. Also, if you have the Turtle Dove form, you'll want to do your best to take as little damage as possible, keep the Turtle Dove form and use the P icons to recover your extra hits when you can.
I can't avoid the face here, so here's what happens when one of the huge faces near the beginning of a level sucks you in: you'll be in an underground area. In the areas where the blue enemies fly up, hang back and shoot yourself a path to the other side, then zoom forward when the blue enemies close in. When you see the huge worm, shoot it in the head. As for the forks in the road, always take the top route. You'll have fewer problems that way.
At the end, you'll be in an enclosed area where you'll have to shoot all the worms in the head in order to continue on. These worms shoot bubbles that cannot be shot down by your weapons, so be careful. Thankfully, you can switch the direction you're facing with Left and Right on the Control Pad in this room.
There are walls with turrets that you cannot shoot down due to being on the side where they can't be shot down. For these, keep moving downwards if you're moving towards them. Their shots will miss you every time.
There is a turret with a whirlwind that takes you to a bonus area. If you take a hit while bombing that turret, the whirlwind won't catch you if your invisibility frames are in effect. You'll definitely want to catch that whirlwind; besides the obvious bonus area, you'll get a breather from the turrets in addition to all the tense action in this level.
After this, you'll have a few more walls with turrets you can't kill. You'll have to bum rush your way through this, hopefully without getting hit a lot. Watch out for the gray X-shaped enemies as well as the spinning enemies that shoot and run. After this, you have the usual temple entrance situation of bombable statue faces and the dragon before going in.
The temple starts with pink robots and ceiling turrets. Shoot them all down. If you need some P icons, you'll have to brave some corridors and some wall turrets to get them, so move and think fast. There are a few more at the green enemies near the end. After that, it's more pink robots and ceiling turrets before you face the boss.
The boss here has at least seven eyes. Once again, take out as many eyes as you can while taking care of the boss. Once you beat the boss, you'll need to destroy the flashing, fleshy walls behind the weak point in order to get to the other side.
At the other side is a green core. Four fireballs will move towards it. You'll want to avoid these fireballs at all times, whether they are travelling to the boss or being fired at your current position, so get your shots in and stay on the move. Just like with the worm battle room, you can change the direction you're facing with Left and Right on the D-Pad.
Sometimes you may find a black image of the core inside your character's sprite while you're flying around. If you notice this, then you've just found out where the boss is going to teleport to. Line yourself up and get a whole ton of shots, then avoid the fireballs. If you can't find it, don't worry; just play conservatively and get your shots in when you can.
Once you destroy the core, you've saved humanity from extinction and you've beaten Legendary Wings! Congratulations!