The objective of each level varies. Usually you need to kill one or more specific enemies to get a key or to open a gate to the next level. Often you may need to pick up more than one item. Ultimately your goal is to find the seven pieces of the Armageddon Weapon you need to take on the final boss. Typically to do this you need to kill a minor boss that has one of the pieces.
Many levels are more than challenging, especially without the proper weapons.
You'll need to hoard the powerful anti-matter torpedoes for attacks on the large ships so you can grab keys and weapon parts quickly before you are overwhelmed. It takes far too long to do any real damage with other weapons. The problem, of course, is finding enough ammunition. In any case, you will not find this game easy unless you are awfully skilled at this sort of game. Indeed, you'll die a lot until you figure out how best to go about a level even on the easy setting.