You have to make it through all 6 missions without using more than 5 continues (you get 3 lives for each continue). Patience and practice are going to be your best friends on this run. Tanks are going to be your best friends in the missions as they will not only give you more fire power, but also allow you to take multiple hits of damage before they explode leaving you defenseless again (and make boss fights MUCH easier).
Bosses will obviously be your biggest threat to keeping your lives intact, so here are tips on how they attack and how to defeat them (hopefully) easier:
Mission 1 - Level Boss: The boss is a cannon type tank that is built into a hut like structure. It has 2 modes of attacking you. The first one is that it will fire 3 lobbing projectiles at you and then repeat the same attack after those have fallen. These are slower moving and easily avoided just by moving back and forth in between them, just make sure to keep firing on the boss in between avoiding the attacks. After it takes enough damage, it will switch it's attack to a high cannon beam followed by a low cannon energy ball attack. All you have to do is duck when it is firing the high beam and jump over the energy ball. Just rinse and repeat while attacking until it falls.
Mission 2 - Mini-Boss: After fighting the boats, you will come to a house where the roof will blow off, exposing a large tank. The tank fires very slow moving cannon ball type attacks, but fires them fairly regularly. Just aim up and keep firing away at the tank as you move to the side to avoid the attacks. For a very easy time with this boss, make sure to pick up the Shotgun power up from the last boat your defeat and stand up the tank firing up constantly as you should be able to beat it before one of it's attacks even gets to you (should only take about 7-8 shots from the shotgun).
Mission 2 - Level Boss: The boss of this level is a plane type vehicle you will fight while riding on a train car with rising and lower platforms. The boss has 4 different types of attacks. It's first one is it firing missiles at you that will either spin around before coming at you or just head directly at you. All you need to do is duck under them if they aren't coming at you along the ground or jump over them if they are ground level. During this attack phase, occasionally a solider will pop out of one of the doors and lob grenades at you so move towards the right side of the screen to avoid them easier. After you do enough damage, it will throw out a lot of mine-like grenades of the back of it. Just stay to one side and shoot at them and avoid them as best you can. After that attack, a general will come out of the door with a rocket launcher and start firing at you. It's best to try to stay under him so he only fires straight down while moving back and forth to avoid the shots. Just keep firing away until you defeat it.
Mission 3 - Mini-Boss: This mid-level boss is a guy with a machine gun and takes place on a mountain area with different levels to jump up to and to drop down from. His main attacks are his heavy machine gun fire and knife attack when you get close to him. Just stay on the top level and keep firing down at him while avoiding his knife attack if he gets on the same level as you until he dies.
***After beating the mid-level boss, try to collect as many grenades as possible throughout the rest of the level and use them minimally if possible as it will make the end level boss beyond easy***
Mission 3 - Level Boss: A giant tank will appear at the bottom of the screen for you to fight. This can best the easiest boss fight you've encountered yet if you followed the above advice about grenades (which should be easy enough to do). Once it's mostly on the screen, dunk in your tank and start throwing your grenades at it as fast as possible, moving backwards a bit after every few thrown (if you don't have your tank still then just lob grenades normally while moving back as well). If you follow this step, the tank should honestly fall before you even have to worry about it even attacking you. If you do not have enough grenades to defeat it for some reason, then fire away with your tank or if you no longer have that, then the prisoner you save right before the boss comes out gives you a rocket launcher, so fire away while avoiding it's projectile attacks. The tank attacks with a rocket launcher blast from the top launchers and shoots at you from the turret on the back.
Mission 4 - Level Boss: There are two tank bosses at the end of this level, one that rides on the upper level and one on the bottom. As long as you still have your tank, this battle will be very easy. When entering the boss area, take the ramp to the lower level and move to the right of the screen as the bosses come on. Stay to the right until the tanks locations are almost both in the middle of the screen and then move as far to the left as you can so you are right against the lower tank and fire away with your regular cannon while ducking down until it dies and then turn your attention to the upper one while avoiding it's missile attacks (just move further to the right for the most part and you shouldn't even have to worry about it) until it falls as well.
Mission 5 - Level Boss: This boss is a tank that raises up to reveal a fire cannon underneath it after it takes enough damage. It's main attacks consist of firing a barrage of missiles, a set of 4 lobbed fire-cannon balls, the fire cannon (while throwing the previous fire-cannon balls as well) and finally homing type missiles. When you first start the fight move in close and duck down and start lobbing grenades at it relentlessly while avoiding it's attacks by moving back and forth if necessary until it lifts up to expose the fire cannon Once it does, start throwing grenades at the fire cannon while avoiding the other attacks until it explodes (if you do it quickly, it won't get a shot off). Once the bottom fire cannon blows up, it will drop 4 prisoners that will give you fuel and other things for you tank, so roll right underneath the tank and collect them while firing and lobbing any remaining grenades you have at the tank. While you are doing that, be careful as it will be begin firing off missiles that will home in on you under the tank and can do massive damage, so try to shoot at them and keep your focus fire on the tank to bring it down before your tank blows and it starts taking you down.
Final Mission Boss: You will fight another helicopter with a general hanging out the side who has a rocket launcher. The helicopter will begin by firing at the ground in spots on the ground moving towards you, so jump over them and try to get under the helicopter and just unleash on it. After that initial attack, the general will begin firing rockets at you, so if you are under the helicopter, start moving back towards the left side of the screen while still firing at the helicopter while avoiding the rockets. After he finishes, the front nose of the helicopter will open and fire out 3 missiles that you will fly around before finally dropping to the ground, but you can shoot them before then so try to take them out and return your fire back to the helicopter. The bottom hatch of the helicopter will then open and the helicopter will raise up to the top of the screen and begin to drop bombs as it moves across the screen. An easy way to avoid these I found is to exit your tank right before the bomb drops on to you as you avoid the damage if timed properly and then you can return right back into your tank to resume attacking. The boss will then repeat the front nose missiles attack (more of them this time and you probably won't be able to shoot them in time so you can use the exit vehicle trick listed above to try to avoid the damage), then the general will fire rockets again (if you are further to the right of where he is, it doesn't seem like he can fire or hit you, so that's a good place to be) and then the bombs dropping out of the bottom again. He will keep repeating different attacks listed above, so just avoid them as you did before and keep firing away at him until he falls.
This is by far the hardest fight, especially if you don't have your tank or lose it during the encounter. If you don't have it, then you need to use the platforms to your left to jump on and to jump over the missiles and make sure you just keep moving and making your main priority avoiding attacks and return fire when you have a moment in between his next attacks. He takes A LOT of damage before he falls, so just keep plugging away and hopefully if nothing else, you have most of your continues left that you can use if need be.