The entirety of this route stretches along a river. As result, it's primarily filled with water. You'll definitely want to use an Aqua Lung on this stage. Not just to clear the stage more easily, but to locate the two secret underwater chambers. It's also likely that you'll use up an Aqua Lung, so it's a good idea to have a spare in reserve.
Assuming you entered from the left, watch out for the trio of looping enemies that greet you, and then put on an Aqua Lung if you have one. Then jump into the water. Ignore any enemies that occupy the sky and swim down along the bottom of the screen. Eventually you will locate a single screen with two hearts and two gold bars on the floor. Collect them and swim back up. Continue to the right, swimming along the bottom. When you get close to a small platform on the surface of the water, you will discover another chamber below the platform. This chamber is home to one of the Governors.
Before the battle begins, Bang inquires about the number of Medallions. Killer Shark explains they're not limited to the number of Governors. Then the fight will begin. Compared to some of the other governor battles, this one is fairly easy. Killer Shark likes to appear somewhere in the room, and summon a column of three fish which she sends in your direction. All you have to do is continue to fire so that you hit her in the head, wherever she reappears, and shoot or dodge the fish that she fires. If you shoot her consistently, you can defeat her in under a minute. Then she will explode and drop a medallion. Collect the medallion to regain your health and then return to the surface.