Repair the energy bridges is a mission in Going Commando, taking place in the Maktar Resort, Maktar Nebula. After Ratchet competed in the Galactic Gladiators battle, he returned to a floating platform. In order to return to his ship, he had to repair the energy bridges leading back to the walkway.
On the platform, use the Electrolyzer in the nearby port by pressing when prompted. To complete the Electrolyzer puzzle, allow the blue particles to pass through the connector without hitting the side. Ensure this by pressing or to flip the connectors just as a blue particle passes through. All connectors will be flipped at once, so pay attention to the entire board. After all connectors are removed, the puzzle is complete.
Any energy bridge will open, so cross it to reach another platform. As you do, a cutscene will commence. Following this, you will gain coordinates for Megapolis, Endako. Complete the next Electrolyzer puzzle first to create a path back to your ship.
If you have not already done so, complete the mission "Find a way to the Thugs-4-Less Jamming Array" here on the Maktar Resort first. Otherwise, head to Endako for the missions "Rescue Clank from the thief" and "Visit Clank's apartment", as both are crucial for progression.