rockaman
Regular
I think I've read a hundred times already that there are five. The Giant Bomb quicklook also shows that levels change quite a bit when you play them on harder difficulty, with additional enemy types showing up.
There are 5 stages.
The enemies have "permutations" as you go along the difficulties. And there are some added enemies as well. It's hard to keep track of them though, like which ones are new, because there is so much going on.
Some of the enemies on normal mode are immobile, while on the veteran mode they move a bit. And some change behaviour on veteran mode at some point and move faster.
You also lose the multiplier much faster on veteran mode if you don't shoot anything for too long.
Max multiplier is 10x for normal, 5x for easy, 15x for hard, and 20x for hardest. On hard you aggregate multiplier faster though, even though it's easier to lose.