Alright Triple Factorial, I just watched your replay. If I may, I would like to give a few beginners tip that may help you:
Learn when to focus and when to not focus
I noticed that the only times you focused were when a boss was on the screen. In fact, it is highly recommended that you be focused except when you need to move faster. Though you move slower, you also move more precisely, allowing you to do things like collect items easier. A good example on when to not focus is Cirno's opener, which you had a lot of trouble with: Rather than try and dodge the attack she fires directly (which is difficult even for an experienced player), unfocus and move out of the way entirely. Speaking of, this leads me to my next point.
Learn how each attack works
Though it may be hard to believe, Touhou is a lot more orderly than you think. Very few attacks are completely random and up to reflexes; the vast majority of them have some aspect of them that can be manipulated in your favor or learned to ease the difficulty. I realize this is not something to be expected of a beginner player, but it helps to keep in mind that learning how a part works is key to doing it well.
Get off the bottom of the screen
It's true, the olden shmups of yore had you limited to the bottom of the screen and restricted to horizontal movement. However, Touhou gives you complete freedom to move around the screen, and it is necessary to capitalize on it. When a boss drops their power items, move up to catch them, rather than wait for them to fall (which by then the next attack is already underway). By stage 4 using the entire lower half of the screen becomes invaluable to dodging attacks, so it's best to learn now.
Hope that wasn't too big a mouthful. ;^_^