I got the feeling that it is essential to get very good results (in terms of money collected) in every episode.
I started episode 2 after finished episode 1 with a score of about 80000. The weapons I could afford for that money hardly made a dent in the enemies. So I replayed episode 1 and finished with about 110000, which made the beginning of episode 2 easier, but still really hard. I think under 150000 it hardly makes sense to continue to episode 2.
One thing that sometimes you don’t notice is that you can upgrade your weapons in the story mode store (arrows right/left on the keyboard, or in the panel under the ship display).
It really doesn’t get hard until episode 4, so keep going!
What you might want to do is find some secret levels, collect fruit/gems/etc. and just try different weapons. Also, the generator is key, as some higher tier weapons will just eat your power and you’ll be stuck with a low rate of fire.