Hope this helps...
Finished this game quite a few times (15+ years ago and recently too). Shouldn't be anything too difficult, it's not really until after level 5 that sometimes it can be a bit hard to work things out. Here are some basic control instructons that should help you get through it (note that this was taken from the SNES version):
"There are four different jumps. You can easily jump straight up by pressing up on the control pad. If you hold up on the pad you can climb to a ledge above. You can leap two steps forward by holding the A button and pressing up on the control pad. This is useful for jumping between ledges, or over dangerous mines. To perform a long jump you must run a few steps, then hold up on the control pad. The final jump is the least obvious: if you have at least four steps of space to run, you can run forward and leap to a ledge above. Do this by holding the A button and tapping the control pad in the direction you wish to run, then let go of the control pad and keep holding the A button. Once you grab the ledge you can hang as long as you hold the A button, climb up by pressing up on the control pad, or let go of the ledge by letting go of the A button.
To use an Item you must select it in your inventory (accessed by pressing START), then hold the B button until the item is used. You’ll receive a force field in the second stage. Leave the force field activated in your inventory when not using other items so you can use it with little effort. When shooting enemies you can rapidly press both the A and B buttons to activate the force field while shooting. The force field only appears for a moment, so try to time it when bullets are headed your way. Even more important than the force field is your shield. You have it when you begin the game, and retain it throughout the game. You can receive up to four hits before the shield is worthless and the next bullet claims your life. The shield will not protect you from high falls. Once your shield hits zero and you’re hit, you die. Then you must restart at the last password or Save Pump. Therefore, it’s important not to get hit, but even more important to recharge your shield whenever possible. You can recharge your shield at the Energy Generators, which are found throughout every stage. Remember where the Energy Generators are, because you’ll want to return to them whenever your shield is low."
I believe you may need to have the joystick plugged in the other port. Could be wrong though, haven't played in ages. Can check when I get home tonight...