Sometimes the game gets confused if you held down a key while dying to enemies, I got teleported to the middle of the map and my input was locked, so it went forward without input from my keyboard. Also, I can't dash and I don't know why.
And I find it hard to time jumps at the end of a platform, It seems that I'm further forward than I am, resulting in me plummeting to my death even tho I was spamming the jump key. I think that was the main reason to my deaths :P
Otherwise, the game looks really good for being made in a month. You sure cut down time of modeling/animations by making it a fps, but I guess that's good as then you can spend time on game mechanics and other things that need more attention - f.ex. level design: where I think you did a great job.
Although there was only one path to follow, you made sure we could use different tactics to get around an obstacle and that makes it more enjoyable in my opinion, as you could challenge yourself to do speedruns or no-shooting runs if you really wanted to.
Apart from a little oversized hitbox, I'd say the game is perfect; considering time limitations and being just you making it :)