Don't waste your bombs, try and save them for when you get into tough situations later in the game where they can get you out of trouble.
Health Pick-Ups
It is vital that you collect the health pick-ups as they become crucial when you reach the harder levels. It is worth taking the hits recovering them as the boost that that they give is considerably more.
Strafing
If you strafe across the screen when a barrage of alien bullets are flying at you you'll be able to destroy a couple of enemy ships while dodging their fire.