Skull Man's stage is mostly a straight-up action stage, and there's not a whole lot here you haven't faced before. But there are some threats you do need to be aware of.
The main new threat is the Skull Joes. These guys throw bones at you, and a hit with your cannon will simply collapse them, and they will soon regenerate. To put them out of their misery once and for all, use a charged Mega Buster shot.
Use Rush, your items, and your Master Weapons wherever you think you'll need them. Just be sure you save that Dust Crusher for the boss; it will ease the experience considerably. If you're willing to make some detours, you can find TWO Energy Tanks.
Most Mega Man games have a "shield" robot, and in Mega Man 4, that honor belongs to Skull Man. He constantly equips and unequips the shield, and moves rapidly, jumping high all the while. Focus on dodging him and his attacks, and fire with the Dust Crusher whenever you get an opening. If you got those Energy Tanks earlier, you can use them if things start to look grim.