Hello. I made a bunch of videos of me beating the first 4 bosses perfectly on Unlimited difficulty using Type III ship. Here I wrote the strategies I've used as detailed as I could.

I had quite some trouble beating the fifth boss perfectly and decided to quit trying completely. I have no way to practice right now, so the last video is delayed indefinitely...

Like I said before, without Type III's high movement speed and damage I don't think this is possible at all. Type I feels much easier to control, but you gotta drop that crutch sooner or later. Stay as close to the boss as possible for tons of damage and try to fill the secondary weapon's bar entirely before releasing it.
Also, make sure you have vertical synchronization DISABLED, otherwise you'll get a terrifying input delay (hello touhou). If your game starts going crazy slow, play with the graphics settings a bit.

1st boss is about targeting his middle part as much as possible. You stay in the direction opposite of where his main gun is aiming and you just have to dodge the blue bullets by moving from side to side a little.
In the next attack you gotta stay as close as possible and again target his main gun, because if you destroy another part of him he'll change his attack pattern and that might make the fight a bit harder. The trick is to stream the purple walls of bullets by dodging through the gaps in them. Big gaps come out quite often, so you have to just keep calm and wait for that gap.
During the next attack go to the very bottom and focus on dodging the attack that comes at a 0 angle - you stay right next to it and the openings will be right there. That attack is also pretty much the same every time.

2nd boss took me the longest to beat. You have to destroy two legs on the same side no matter what, or green balls will get you. Don't focus your gunfire neither on the main body or the legs - shoot them both at the same time. To make the first part as easy as possible, keep moving close to him whenever possible and remember that the bullets will fly faster the further you are from the source at the moment they're shot. If you manage to get close to him whenever he hits the wall with a leg, the bullets released will fly slower and it'll get a bit easier. The trick is to alternate between dodging the bullets flying from the left and then dodging bullets from the right - this way you have to focus on one side of the screen and you can completely forget the other side until you dodge the other, which makes it a lot easier to stay calm. You have to switch a lot and quickly in this case, but looking right in front of the character and watching all the bullets at the same time is a big mistake. The whole part isn't random - it depends entirely on where you stay and how you move, because all walls of bullets use the same pattern. I prefer to do a little circling maneuver on the left side.
As soon as you finish the first part you move as close as possible to make bullets slower and move to the other side. When he shoots that big wall of blue bullets you have to stay in one place the entire time - preferably in the middle. Move a bit to dodge the purple bullets and unleash all you've got, then move into the gap where the destroyed legs have been because that's the safest place to stay.
All the following attacks are very easy to stream - just move a bit to the side every time he shoots and you don't even have to do any dodging maneuvers. I have no idea about how lasers work, so just remember to move forward as far as possible and pray he doesn't shoot a wall of lasers too big for you to dodge.
The last part is only about killing him as fast as possible until he starts shooting lasers again. Stay in the middle as close as you can and move through the openings in the patterns. Don't stop or hesitate or you'll be too slow.

3rd boss is all about memorizing. During his entrance deal as much damage and look for the opening in the pattern - it's always there, but sometimes you'll be to slow to notice it. The next part is pretty much the same all the time - I'm not sure if my method is the fastest, but it's quite safe and easy to dodge. Just remember the place I stay at.
Here comes the second stage. The trick is to stay underneath him and try not to be in the places where you have to dodge the diagonal shots, because they're much harder and you will eventually get in a very bad spot. You'll see through the pattern and will find where to go, but only if you focus on staying right below him all the time. The part where he starts rotating is just about practicing as much as possible - you will almost always get in the same situations. It's the part where you NEED to know the specifics of your ship's movements and speed. Find a gap, move through it at focused mode then shoot. Repeat over. Your success depends entirely on how quickly you can find that gap and realize when you have to start moving through it and how. That's how you get good at shmups.
I'll stay off from the start that the last part is insanely difficult and that I just prayed for luck (which came). The concept is to again focus on staying directly below him, then you'll notice that there's almost always a very small opening for you to get through. You just remember all you know about dodging, take a deep breath and follow the plan.

4th boss is my favorite. You have to immediately deal damage to both parts that shoot rockets. Then you destroy one of them and start shooting him in the middle (he ALWAYS moves the same way, just remember his movements and timings on the laser, then you just have to dodge the bullets he shoots at you) and pray he doesn't shoot rockets from the remaining one and you don't touch them. As soon as that part ends, you destroy the other rocket launcher and that clears the screen from bullets. Then you have to remember how he moves when he shoots a wall of bullets and repeat that same movement when dodging through the center of that wall.
His second stage is why you'll love Type III. Dodge whatever he shoots by going to one side - unleash everything until you kill that weapon - repeat on other side. NEVER start moving until you kill the weapon on that side. Lasers are the worst, so don't start dodging until you're sure it's gonna be dead.
The last side is just fun - stream his bomb dropping attack, dodge the little walls of bullets between the lasers, then repeat.

5th boss is boring. Even though I don't have a video, I can still share my strategy for him.
When fighting drones, you gotta control your secondary weapon. Keep it charged, move to one side and release it - that should kill a bunch of drones and clear that part of screen from bullets and you'll be able to repeat the process of the other side.
First stage, you dodge left - right - left right and then shoot him a bit, all while staying very close. He should be dead before he'll start anything harder.
Second stage, I've never been able to beat without dying. The theory is to maximize the damage as much as possible until he changes his pattern to an extremely difficult one. Move forward and diagonally when he sprays bullets from both sides, then you'll be most unlikely to get hit. He usually survives with something like 1 hp. Maybe you'll be able to beat that part without dying. A left - right maneuver should work, but I can't get the timings right.
During the third stage you have to control your secondary weapon again. Move to one side, release it then move to the other side - that should minimize the amount of lasers you'll have to dodge when moving, and scary circles which dead drones release will not bother you at all.
I believe that when he starts jumping sometimes the bullets fly slower and you get an easier time dodging to the other side. Try not to wait until he squeezes you to the wall - wait 1-2 jumps for that easy jump, then dodge, otherwise there'll be too many bullets or you'll hesitate.

Just in case you didn't know, there's an extra boss which has 2 stages. You can fight him if you've never used a continue and then fight his second stage you didn't use a continue during the first one. The strategy is to not get hit by bullets. It's hard to give any tips because usually the whole screen will be full with crazy flying bullets and you just gotta focus on not dying.
The trick to his opening attack is to focus on looking at the whole screen at once and trying to find out where the biggest and the smallest masses of bullets are going. Move to the place where the amount of bullets will be the smallest and keep looking ahead to predict where you'll have to dodge later. As soon as he starts charging his laser, go to the very bottom and stop (this is very difficult depending on where remaining bullets are), then upon release start moving in very small amounts to the side - this way the laser will be right next to you but the blue bullets will fly in a way that will leave you an escape route for later on. That whole part is the hardest of the first stage, so as soon as you beat it you'll have easy time. Repeat the process with the remaining laser shots, then circle once around the boss to make the following attack a bit easier. Dodge the changing patterns while staying right below him. When he starts shooting lasers again, move to the opposite side below his movement path, wait until he shoots all he's got then fly upwards and to the other side then repeat. By the end of this he should be dead (not really).
Now it gets crazy. During the first part, stay parallel to the boss. During the second one lure him into the bottom of the screen, so the bullets he shoots disappear below the screen and you don't have to dodge anything. When he starts shooting rapidly, you just stream and change your course to the other side during the small gaps when he's not shooting. At the very end, you just gotta look for the little gaps and fly through them to victory.