The first cavern should be used as a training ground to help you get used to the controls and the way that Layla moves. When you encounter a group of four crates in the floor, learn to use your grenades to blow up the crates and collect the contents. When you see two columns of five crates stacked high, learn to press down and jump to reach the highest crates and shoot them open. Near the end, you will encounter what appears to be a dead end, with a block preventing you from falling down to the floor below. This is in fact not a dead end. You can press down at this location and warp to the floor below. Learn from this experience and never assume that you are stuck in a situation such as this. The entrance to the secret room of the first cavern is actually located right at the very beginning. Instead of running forward, push down and an elevator will take you to a room. The message on the wall is a hint about the location of the password disk, which is located near the top of the fortress.
As you might expect, the first fortress is the smallest and simplest of all the fortresses. You will explore three full hallways at the most, not including the password disk hallway or the boss hallway. The password disk can be easily found if you continue to ride elevators up, but you can also drop down to the lowest level, and ride the elevator to the very top if you'd like to explore a different path. After you collect the password disk, you will be returned to the entrance of the final hallway that leads to the boss.
The first fortress boss appear to be a large bipedal alien, and he's not at all happy to see you. However, he happens to be rather weak. In fact, just one hit from an Ax will destroy him. Switch to your Ax weapon after you shoot down the tiles that lead to his chamber, and prepare to do away with him in one throw. As soon as he is defeated, collect the food he leaves behind and prepare for the first bonus round as you fly off to Asteroid 2.