The patterns and such certainly are not designed to be handled with a keyboard. Particularly hard mode, which is my doing, and which was entirely tested on a controller. The game is stuffed with bullet-hell elements at it's higher levels of challenge, and that genre is one of those where a controller of some sort is pretty much considered a requirement. For a game with those elements, keyboard controls simply don't allow for fine-tuning your movement in the way that's necessary here. At least, not in comparison to an actual controller.
Now, the 45-degrees bit, by which I assume you mean 8-direction movement (the only type that's possible with WASD controls), the game IS tested for that. When using the controller to test and tune these things, I use the dpad, actually, not the analog stick, when it comes to movement. It's an old habit: Most of the games that inspire much of the design in here actually ONLY use 8-way movement... no analog. So the game ends up tested in that way when I'm working on it.
Now, does all of this mean that Hard mode is impossible with a keyboard/mouse? Nah. But it certainly limits you, yes. Even for someone who is very good at these, this would be true. Even an analog stick will give you better control. If you have a PS4 or Xbox 360/1/whatever controller, I'd recommend using those instead. Also, regardless of wether or not you're using a controller or keyboard, look in the options menu and make sure that "shmup movement" is turned on. This removes the bit of momentum that the mech otherwise experiences, causing it to stop dead in it's tracks.
Though, there's also the fact that you're leaping into Hard so early. Hard mode is designed for those that have completely mastered Normal mode.