Wow! Great polish on this one, I was immediately impressed when I shot the first bullet.
I think that the tutorial segment could be converted from text to some pictures showing the actions, since there is plenty of room on the walls to have them "carved" into them. It can really help with the intuitiveness in a tutorial.
When doing the first level, I thought that the player speed was way too fast, and found it hard to make small adjustments. In which I was going to note that their acceleration should be lowered. That was until I got to move fast for awhile, and I figured that this was a game that wanted you to move fast. Since the movement felt really good when you were going.
But, I think there is a bit of an issue here, Speed Vs. Precision. There are some really precise saw placements which can make the player come to a halt if they want to get past it, especially if they are unfamiliar with the movement. Having precise jumps isn't a bad thing, but having them so early before the player knows really how to move yet can make it hard for them to enjoy the game.
I think that the general amount of precision should be lowered, and you should let the player fully embrace moving at full speed. Having long straightaways and empty segments for them to just use their speed. This is why level designing for fast speedrun games is so difficult, since they need to be very large to compensate for the speed the player can move at. (Often resulting in a lot of work for players to blow through a level.) But, if you get the player to keep trying to get a better time, that is where you get your value.
I think speedrunning games are at their best when you can complete a level, see the time, and think "I can go faster." And while I did think that I could go faster on some of these levels, they were just too difficult for me to want to do them again, let alone find a optimal route. Having difficult levels is not a bad thing, but you should give the player some levels beforehand with very little ways to die. And then they'll try to get better times and not have to restart the first jump a ton of times, thus learning how to move well.
When designing the first few levels, you should make things that are super simple to you. Since you are the best player of your game. Think of how in other games when you go back to the first levels they are just super easy, that is you.
Many people say that there should be more bullets to shoot. And I think this is a difficult decision. Since if you give them too many, they can just go wherever they want. I do also like the idea of having to plan through where you are going to reload, and where you are going to use your shots. This is definitely a line you will need to test a lot for how many bullets are needed per level.
The amount of times I restarted instead of reloaded was... too many.
How many levels were there? I got to 5 and died in the very last spot.
Great work!