The first Plumbers' Badge is located in the large enemy encounter area after the electrified pipe and the three acid pit traps. Just smash the machine that it is encased in and collect it.
After defeating the two giant snake heads, a ramp will appear that Cannonbolt can use to ramp across and reach the U-shaped cave. The Plumbers' Badge is at the end of the cave before you jump back across the acid pit.
This Plumbers' Badge is just after navigating the two floating platforms that are created by throwing fireballs at the two explosive containers. Turn to the right just after reaching the other side of the acid pit and you will see it.
The next Plumbers' Badge is fairly easy to spot. It's at the end of the catwalk that you need to go down to open the door after the three opening platforms. Just jump past the last two acid gushing pipes to reach it.
This Plumbers' Badge can be easily overlooked due the fixed camera angle in the area. After heading through the door leading to the factory that contains the Cannonbolt burnout puzzles, turn right and walk into the corner to collect the Plumbers' Badge.