Well, I just played your game for four straight hours. I HAD to beat it with no deaths, and when I did I wanted to screenshot it for you, but while I was basking in the glory the message disappeared! Please, make it so you have to click out of that! People are still coming off of their adrenaline highs and wont be able to focus enough haha.
Anyways, if you couldn't tell, I love your game. Samurai Lantern is probably one of my favorite games of the year (Honestly. This game is fantastic.). It's so tightly focused and so good at what it does! The screen shake when you hit an enemy, the excellent stage set-ups (I love how the stages wrap around and how that affects enemy pathing. It was brilliant when I figured that out.), the gorgeous retro graphics. I even enjoy the three stage length. This game is like portal where it doesn't stay too long, it just puts forth all its ideas in a coherent fashion and lets the player decide how long they want to spend with it. It's simple and quick, and that is what makes it good for spending hours on.
I'm hesitant to even offer suggestions because this game is beautiful just the way it is, but if I could offer three things, it would be these:
1) I'm just going to echo what other folks have said about the arrow keys on the controller. Please make that an option. I had more than a few deaths due to analog stick inaccuracy.
2) An optional speedrunning timer and a local best times list would be fantastic. This game is going to live on my desktop now and I'd love some kind of persistent score tracking.
3) I know I said its short length is a plus, but any way to get new levels in there would be awesome. Maybe some sort of rudimentary level editor or something along those lines. I'd love to play with all kinds of different set ups well past the three you've included.
P.S. Thanks for making this game. I don't know if it will be widely liked, but just know at least one person loves it. I'm going to shoot you some money when my next paycheck comes in so you can keep up this quality work. Cheers!