There are three types of enemies that you will encounter in this cavern. The small creatures like to alternate back and forth between running along the ground and running along the ceiling. Then there are slightly larger green alien creatures that charge forward along the ground. And finally, there is the floating force field from the last cavern. You can destroy it if you shoot at it while it's on screen, but it takes quite a number of bullets and is best avoided. Early on, you will find a large cache of crates from which you can obtain items. Shortly after that, you'll have to warp up to continue on. The entrance to the secret room is one of the tricker sections. You'll have to stand on some of the blocks to make them disappear, then shoot out the blocks along the bottom, and headbutt the ones above you to gain access to the secret room entrance. Before you step on the far right blocks which dissolve beneath your feet, push down to access the elevator. This secret room tries to present you with a bit of the layout of the fortress, but it's not extraordinarily helpful.
Once again, the forth fortress is fairly complicated, but you can bypass a portion of it if you correctly locate the placement of the password disk. It is easy to miss. As you begin to progress through the first floor hallway, you'll need to look for the first elevator shaft. Make sure you stop at the first door you come to and press up or you will miss it. From there, you are warped to the end of the first floor hallway, and you have no choice but to travel up to the second floor. Run to the end, and drop down to the first basement, then run to the end of that, and drop down to the third basement, and you are on your way to the boss.
This stage has one other odd feature, but you will not be able to investigate it at all if you properly go for the password disk. The only way to see it is if you return to the Asteroid afterward (or skip the disk which isn't recommended). If you travel all the way to the top floor, you will come to a section in the middle with two columns of destructible blocks. The left one can be broken all the way down to the gap in the floor (with grenades). If you make a whole for yourself to fall through, you will wind up in the fourth basement. While it's a neat trick, and the fourth basement has a good number of crates, this will actually cost you more in the long run because of the penalty for falling through the floor. Also, if you're very low on life (flashing screen), this could actually kill you. It's more of a novelty than anything useful.
This boss looks identical to the boss of the second stage. Unfortunately, it's a lot more resistant to most weaponry. It's really only affected by regular bullets. Your best bet is to use the machine gun. Run to opposite sides of the screen, and fire off a blast of bullets before preparing to run across to the opposite side of the screen. After you hit the boss with a couple of rounds of ammo, it should be destroyed.