The first Plumbers' Badge can be easily bypassed if you're not paying attention. It is on a small island in the middle of the river that you must glide over. After gliding across the river, just turn around and glide down to the island. Then use Spidermonkey to grapple your way back up.
The second Plumbers' Badge is on the ledge to the left of the giant spike pit inside the first set of doors that Swampfire opens. Just glide down as Big Chill to reach it.
The next one is slightly hidden behind some giant flowers in a corner within the temple. It is in the area directly after the Hovering Bioid enemy is introduced, but before entering the stairway puzzle area.
When using Cannonbolt to open one of the oversized doorways you will notice a Plumbers' Badge through a second set of doors that opens, but the doors will close before you get to them. Don't worry though, because you can use Humungousaur to pry that door open and collect your reward.
The last Plumbers' Badge is located in the room with the spiked ceiling. The Plumbers' badge is on the side of the room opposite the exit. Just place the block on the “T” intersections to prevent yourself from being crushed by the ceiling and make your way over to it.