Dr. Cossack lives in the frozen regions of the north. As such, you'll start your raid on his castle by wading through knee-deep snow. You'll soon come to a small tower, flecked by snow. A slinkie-shaped robot is descending, and it will take several shots from the arm cannon to disable him.
Once you're past that, you can continue forward, to another tower with the same type of enemy. Beyond that, there's a more extended tower. On this one, you'll find three more of the slow-moving enemies. None of this should lead to any damage to your life meter, and you can hop from the tower to a ladder and climb into the next screen. Make sure you're moving at a run and jump from the very edge, or you'll fall into the pit below the ladder. If you're not sure you can make the leap, go ahead and use the Balloon item to make it more safely.
The next screen above has two of the rolling enemies familiar from Ring Man's stage, and from the Drill Man area. You can slide under the first opening, lure the first one down to your level, then slide back under and shoot him from a distance. Then climb up near the top, stand where the ladder is, and jump and shoot whenever the machine is far enough away that you can safely do so. Again, you should be able to navigate this area without taking damage.
The next screen up from there takes you to the area's rooftops. As you push toward the right, you'll see a bone-tossing robot. Take it out with a charged mega buster shot. As you may notice, you're on a rooftop of sorts. There are gaps between ledges, but you don't want to just leap over them right away. Enemies come flying out of them, like in the Dust Man stage. Take out an enemy, then quickly cross. Keep moving to the right over the rooftops, until you come up against a ledge with several levels. There are several paths you can slide, but you really don't want to as they lead right to a bottomless pit. Instead, climb to the top of the ledges as you press toward the right. Note that the ledges are slippery, so you don't want to slide off the end.
To the right, you'll see a bone-tossing robot. You want to make a long jump over the gap when it's safe to do so, without his bone hitting you. Not only that, but another of the enemies likes to come out of that pit. You should be able to clear both hazards, then climb out the ladders and take out your bone-tossing friend along the way. From there, climb the ladder into the next screen.
You're now at a series of screens where you must use the Balloon adaptor to reach various ladders suspended over the bottomless pit beneath. Place them so that you can ride them upward to the ladders, which you should then climb to scale the castle's face. Near the top, you'll come to a series of ladders with steel traps. You must climb up the right-most ladder, into the next screen, then climb down back into the previous screen, and drop from that ladder to the next one to the left (do so from too low on the ladder and you'll fall down, which is bad), which is patrolled by the steel trap jaw. Climb upward through the gap in the teeth, just after it has clamped shut and reopened. Repeat this for the next jaw, until you're on the left-most ladder and can climb up to the next screen.
Here, you're going to see another of the chubby, pogo-like enemies. Take it out with some quick shots, or slide under it when it jumps high enough, and pass through the gate to this area's boss encounter.
NEXT: Stage Two