Hints

You think I'm going to tell you how to beat the game? Ha! I had to figure it out all by myself, and therefore, I think everyone else should too. ;-)

Ok, not really. The master plan is to get a major part of the world Kobo addicted, so I guess I should offer some help for those who can't seem to get started quick enough. I'll add things here as they come to mind, or when people ask and I have sensible answers.

Objectives

Destroy all fortresses on a stage to complete the stage. A fortress is destroyed by shooting it's core. (The yellow/purple ball in the middle.) No need to shoot all the blue nodes first, if you can get right at the core! Note that it's possible (required even, on a few maps) to navigate into bases.

General

Use the keyboard, or better, a serious digital joystick. Arcade control panels should work pretty well, but they're rather expensive, unless you buy separate joysticks and buttons and build your own control panel
When controlling with the keyboard, use the arrows or the NumPad to control direction. Fire is on all CTRL and SHIFT keys.
Shoot everything that moves! And everything that shoots back! And... Just shoot everything, ok? :-) Everything that blows up counts to your score, and at certain intervals, you get extra ships. (Yes, you'll need them.)
Don't look too hard at individual enemies and stuff. Try to "just see" the whole screen. Some enemies and bullets move faster than you, so you can't escape by going the other way. You have to be prepared to dodge things from any direction at any time.
When there's too massive resistance, try a more defensive approach! Many fortresses pump out large numbers of dangerous enemies when you get close, so brutally mowing them down may not work. Use the traditional hit'n'run strategy, at least for starters.

Enemies

Big Ship Just as tough as they look, and packing quite some firepower, these tend to show up if you hang around for too long. Try to get the job done quickly and be off for the next stage before these show up!

The dreaded blue ball Those @£$!#% blue bombs that float around and explode in your face; they can't see very far diagonally. Try to take advantage of that by moving diagonally. This is easier if you fight the bombs in open areas where you can maneuver freely.

Boomerang Fighters These may appear relatively harmless at first, but after a while, they speed up and start circling and firing at your ship. Get out before the rings of bullets lock you in! Don't let too many of these ships fly around. Take a moment to hunt some down before you go back to attacking the bases.