First, if you want to skip the current level, press "P" (for pass). Anyway to beat the two levels:
Level One:
Enemy numbers are directly related to your score, as is the state of your weapon. Eventually, your only enemies are the flying saucers that come from behind you. Just stay halfway up the screen and get behind one as it passes. Shoot it when it gets to the top of the screen (and no sooner!) and it will release 5 mini-buzzer saucers. If you are far enough away, you'll be fine, just shoot 'em up. Once you kill 20 of them, you beat Mission One.
Level Two:
This level is like an update of the first game. After a minute or two of progressively thicker enemies, you will start seeing upgrades fly down the screen. Make sure you get one as you approach the second phase of the level with all the laser turrets and palaces, as they can only be destroyed by the nukes. Stick to one side of the screen, about halfway up and destroy all the turrets on that side as they come at you. After the palace's turrets go by, swing over and bomb the palace as it goes under you, then fly back and continue your bombardment of the turrets on whichever side you've picked. You have to destroy 5 palaces, then you beat the mission.
Level Three:
There's not much to this level except that the tanks can shoot you and you can kill them, plus a little bit of cool scenery. It's incomplete (obviously). If you hold your beam weapon on the tanks for about 3 seconds, the tanks will disentigrate. The SR-71 on that mission flies a bit faster than the 2 planes in the first 2 missions. When the theme music runs out, the level ends and you get to enter your name if you made the high score list. (Level 3 is just a score booster to close out the demo...the mobile tanks are worth more on level 2 and 3 than the fixed tanks.)
"Never completely discount the improbable."
~Dennis