Number of stages: 5
I'm not sure if the first two stages of this round featured in the original version, but the refinery stages were definitly in. Strangely, the final version of Shinobi III references part of this level-the picture icon for the fourth round shows purple pipes and orange-capped buildings, which feature in this round.

 

This level is set in a forest, and you can see some kind of base in the background. The only enemies in this stage are some soldiers, who can throw grenades. There are lots of randomly placed power ups dotted around.

Stage 2 is in a similar location as the previous one, but the enemies here are the powerful robots. There are around 3 of them, but this stage is very short so just run right as quickly as possible to complete it.

Stage 3 takes place at the base, which appears to be some kind of oil refinery. Soldiers and ninjas are the enemies here, and you'll need to use the red girders to progress through the stage.

There are some oddly placed ninjitsu items to collect, and towards the end of the stage there are several girders to walk across.

The fourth stage is fairly short, and has the same enemies as the previous one. About half of this stage just involves running across a pipe.

The boss of this stage is a soldier with a gatling gun, but if you look closely at some of his animation frames, the soldier is actually a robot! This was presumably a tribute to the Master Attacker boss from The Revenge of Shinobi. Also worth of note is that there are a couple of blue buildings in the background which probably shouldn't be there, as they'll move around whenever you somersault jump.

One of the animation frames for the boss has his aiming his weapon straight up. In this GameFan preview, you can see this boss aiming upwards, but he's in a tank! It seems SEGA would get more creative in later builds. Also of note is that every animation frame for the robot form of this boss has him missing an arm -something which is shown in the round clear artwork.