Start the Dr. Aeon Strike Force on Malicious (1 star) Advanced Mode setting or higher. This will cause Golden Brickernauts to have a Power Core Meltdown self-destruct power. Use a Power Core Metldown to defeat Princess Zoe in either the fourth mission, where she first appears (easier since Mr. Rivers will always spawn as one), or in the final mission. You can accomplish this either by using a confuse power, or the Dimensional Grounding Ray (DGR) from the Dr. Kahn Task Force. Additionally, the Golden Throwing Wrench you get as a temp power for completing the Aeon SF will also have the same effect as the DGR. The explosion from a Golden Brickernaut will only affect Zoe if her health is below 10%.

Note that using the DGR will not actually confuse a Golden Brickernaut, only allow their explosion to target friend and foe alike. The Golden Throwing Wrench does the same, though also has a 10% chance to confuse.