The debug mode is mentioned in the game's readme. Pressing F12 or clicking "Player -> Cheat" in the F3 IMGui menu will give you invincibility, which will allow you to shotgun Meiling without having to worry about dodging her attacks.
I’ve found I’m consistently able to beat her with all shot types if I lose all my lives in Stage 1 to get the Full Power item, and then use the invincibility cheat to make sure I can hit her without missing any bullets.
Reimu-Needle is probably your best bet for damage, and I was able to beat her without the cheat engine with it, the fight’s just a bit precise without the cheat.