Excellent fun, the difficulty is a tad off.
I enjoyed this a lot. Upgrading, the story, all of it. But it gets insanely hard, even by medium. Even when I'm shooting pretty well, the (ghostships?) big capital ships can do a lot of damage, and release hosts of ships. Eventually, my ship is always overwhelmed, no matter what I do. As such, the difficulty is more like insane, rather than hard. I notice that in the video you showed us, the guy died at the end?
Anyway. You should certainly make a sequel. Here's things you should change.
Make the turrets have endless endurance. The fact that they die quite easily means that every space near the front is useless.
Add a speed up bullet upgrade, or possibly make the bullets go faster. As it is, you need a lot of skill to use it effectively, and take out fighters. You need to play the game for an hour or two to get the hang of it. Since it's a fairly short game, that's too long. Can you complete medium and hard mode? This is particularly bad for the turrets. The enemy can twist and turn, so they almost never hit fighters.
Add some basic AI control. Not enough to make the game fiddly, just something like "group together and attack" and "lure them away from main ship." and "dogfight."
Put in some more scenarios in the game. Like, fight along side other ships, kill strange boss ships. The caterpillar was awesome, by the way.
Put in a basic shield generator. At the start, you repair very slowly. So, if the enemy attacks you, you'll quickly get low on health even if they only get off a few shots. Shielding would mean you could take a few shots, kill the enemy, and recharge. Unless your foe was able to attack you for long enough to overwhelm your shield, you'd not lose health. That way, easy would be more like actual easy, and the others would be similarly good.. As it is, easy is medium difficulty, medium is hard, and hard is insane.
For people who are playing it, a walkthrough.
Uno. Buy a second fighter ship. It's at the back of ship. These keep enemy fire off your ship.
Duo. Aim two-three inches up or down from whatever direction the enemy is going. If you can take them out quickly, yay.
Trio. Upgrade your main cannon to level two in fire power and rate. Then upgrade it to level three in fire power. Level three can take out small fighters.
Quarto. Upgrade your repair power, first in number, then in number again, then in speed.
Buy a second fighter module, and a second fighter in that, and increase the build speed.
Quinto. Kill the capital ships by shooting at them.
Sexto. Keep upgrading your gun, adding the occasion laser at the back and upgrading damage, upgrading repair, and upgrading your fighters and increasing their numbers. Win.