Star Man's stage is unlike any you've ever played in a Mega Man game before, due to the low gravity. This means that Mega Man can jump extremely high, which is useful for certain situations, but if you're not careful, can kill you easily.
At one point, you'll be in a corridor that has its ceiling lined in spikes. This is an easy place to die due to the low gravity, so be very careful. If you're having trouble making the jumps, take my advice and intentionally get hit by the Space Hard Hats, and then make the jump while you have the temporary invulnerability.
In the aforementioned hall, you'll find the stage's Beat Letter. Use the "temporary invincibility when hit" strategy if you want to get it without dying.
At two points in the stage, you'll encounter walker mechas. These things fire multiple lasers at one time, and stray back and forth. They are only vulnerable in their "eye" on their head, so blast away with your arm cannon. Due to the low gravity, it's not too hard to dodge their shots.
Star Man himself is the game's resident "shield" robot master. He bounces around the arena crazily, sometimes firing the shield off at you, and putting on a new one. He's invulnerable with the shield on, to all but one thing - Water Wave. When he's on the ground, blast him with the Water Wave - it will go right THROUGH his shield, causing damage. If you've got the Water Wave, he'll fall in no time flat.
For beating him you get the Super Arrow, a mostly-useless item, but you may want to experiment with it in later levels.