The first Plumbers' Badge is just after the first encounter. There is a platform to the right after reaching the electrical beam. Switch to Big Chill and float down to collect it. Use Spidermonkey to grapple back up.
In the area where you need to rotate the ramp around and line it up to make it across a gap, move it all the way to the right. Using the Burnout ability as Cannonbolt will launch you over to the platform that contains the Plumbers' Badge. You can then use the ramp on that platform to reach the next platform and continue through the level.
The next Plumbers' Badge is a little tricky. If you open the door needed to progress before opening this door, you will have to play back through the level to collect this one. In the room that requires Brainstorm to reflect the laser beam at the door to open it, open the left door first. The Plumbers' Badge is just inside the door.
While on the Spidermonkey wall climb area, there will be a ledge with a door that is partially opened. Make your way to this ledge, switch to Humungousaur, and pry the door open to collect the Plumbers' Badge.
The final Plumbers' Badge in this level is located on a cliff in the Spidermonkey grapple area. There are two paths that can be taken in this area. The left one will lead to the Plumbers' Badge. Grapple your way up and it is behind the cliff.