Many gamers seem to like saving Drill Man for last, but it is better to go after him first, since beating him will get you the Rush Jet, an item that will ease the pain of many sections of levels considerably.
The stage itself is an all-out challenger. No fancy puzzles or anything like that, just a straight-up, all-out fight. If you have Master Weapons, feel free to use them throughout the levels, but if you have Dive Missiles, you'll want them for the leader. Just keep moving forward, and staying out of harm's way.
There are some sections in the level where you'll need to pull switches (simply by touching them) to make ground appear and continue the level. These sections are pretty self-explanatory. Just stay on the move, and dodge spikes when you encounter them.
Drill Man himself only has two attacks, and he shouldn't be too tough to beat, even with just the Mega Buster. His attacks are drilling underground and shooting out from the ground, trying to spear you, and running around the arena, firing exploding drill bombs at you. When he's on the surface, use your Mega Buster (or Dive Missiles if you have them. Dive Missiles have homing capabilities, so no need for finesse if you're using them.) Just stay on the move, and put more of an emphasis on dodging and moving than ending the fight quickly.
Victory earns you the Rush Jet!