It's a very good game !
There is great animations !
But there is some things that I don't understand.
Why do the tutorial level is called "Training" ? I though it was for training my shooting skills, with different waves of enemies...
And in your description, all commands are not shown (SHIFT for Walking, the Double Jump).
Maybe you should do the tutorial in the first level.
And IMO, Up for Jump, Double Jump and Interact is not a good choice. You should use an other key for Interact, shown over every object that you can use.
After the technical points, we can talk about the game. I think it's cool, i enjoyed it (i've done the 2 first levels) , but I think it can be more intense. For now, I only kill enemies one by one. Make some waves, with 4-5 enemies of different types. I saw that you have already tried that, But there is no lock on theses waves, so if you stop running for exploring the level, the wave is broken.
Nevertheless, the music is good, graphically it's good, the objective of making a retro game is done.
Continue to work on your game !