Here’s a few tips on how to beat the bosses.
The first boss (the three-eyed squid; it’s pretty much the commander of the squids and spitters) is probably the hardest, because it teleports around the screen, making it hard to hit with missiles. You need to stun it with a missile, lazer, or bomb blast in order to damage it with regular lasers.
So, the strategy is to try and save up a few crucial power-ups. Save a lazer beam and a missile, and a lancer power-up. When the boss begins to throw it’s pellets at you, hit it with the lazer beam and then activate the lancer, and pummel it while it’s vulnerable. Then it will teleport and recover from the stun, but as soon as it begins to throw the next pellet, hit it with the missile and then pummel with lasers again. Then use the down time when the boss teleports wildly around the screen to collect power-ups, and wait for it to toss another pellet. Then repeat.
The boss strategy requires that you continuously shoot down new power-ups, which are the larger, fatter mines. They continually replenish on boss levels.
For the final boss (the alien Mothership, the commander of the entire force and the ships), just keep hitting it with all the stuff you’ve got, and try to take down the little helper ships with missiles and such before they can put up the shield. But just concentrate fire on the main boss, and eventually it goes down.
Hope that helps!
Edit: Those little green particles you see in the screenshot above each represent one damage point to the boss. If you can see those green chunks flying off, you know you’re hitting it ;)