You need to buy the Charge Beam from TwoHat Jack and then hunt down these guys:
(The giant one on the right. This is the best picture I could find.)
Charge Beam requires you to hold the right trigger to charge it for a couple seconds and then shoots out a continuous beam for a short period before having to charge again. Maxed out gun almost kills them with one charged beam.
If you have the new Robot DLC you can go to half of the missions to get this done. I prefer Buck National vs Robot Apocalypse. Do the required steps until the Tank Bot comes and then pull out your Charge Beam to kill it. You should be able to get three of them killed per run. So two runs with each run being three minutes.
If you don't have the DLC you can still do this with the base game. I know the final mission "This is the End" spawns two after you destroy a bunch of other Fizzco bots.
If anyone knows of a better main game mission, please let me know.