Though short, this stage can be a real pain in the butt. From the start, you should first collect any special item refills that prove necessary. When you're ready, go ahead and drop down the shaft and aim left.
When you land, immediately let loose with a spray of arm cannon fire. The robot to the left will chuck a huge block at you if given the chance, and it does quite a bit of damage to your weak armor. Once you've taken him out, drop down to the next room below.
Here, you can slide and press to the right to land on a ledge and refill special weapons energy again. Also, you can collect energy pellets to replace any damage dealt by the robot in the previous room. Just watch out for the spikes that line the floor on the left side, here.
When you're ready, climb down the ladder on the room's right side, and you'll find yourself in a room with another of the block-heaving robots. Take him out quickly to avoid more damage than necessary, then drop down again and you'll once more be facing one of the block heavers. Defeat him and start right again, and yet another will appear. Take this fellow out like you did his companions, and then you'll be safe to descend to the next room.
Here, you should just work around the ledge, to the gate on the lower right side. There aren't any enemies in this room, thankfully, so you don't have to move cautiously.
NEXT: Stage Five