Ikaruga - Chapter 1 S++ (Normal)

Final score: 3.474.730
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Second S++ grade I did of all chapters.
The good thing is that the first half of the stage and the boss are laughably easy to chain and deal with.
But oh boy is the second half (starting at 1:08) packed. There is not much risk of dying unlike other chapters, but the speed at which you do them is very noticeable in the bonus waves you get. I spent around 3 hours on this stage as well.

The waves at 1:25 (if you kill the previous enemies quickly) are randomized - here is where your ability to improvise is tested.

You start killing the ring of balls that appears at 1:40 when the last ball of a chain is right in front of you. They move so fast that it's the only way to deal with them properly. Then kill only the tiny white ships (personal suggestion: only do very tiny vertical movements, they're already coming downwards and this way it helps to not crash into them), discharge to deal with the black ones and move to the big ships. If you did it right, you will have time to deal with the orbs that they have on their sides.

Your ability to shoot precisely is also tested for the first time at 1:54. Right at the center.

The upgraded ships at 1:57 intentionally do not complete your chain so you're forced to deal with the tiny ships as well. A single pair from the tiny enemies is enough to complete it. The biggest issue, then, lies in managing both types of enemies at the same time.
It would probably be better if you savestated around here to practice.