Obtain Jenny Millet's security keycard at the end of the REPCONN tour given by the tour guide robot and use it to access the first computer on the left of the locked door from the reception room. Then head up to the second floor and find another computer to obtain further access.
Find all three keycards, take the Q-35 matter modulator from behind a locked (100 Lockpick skill to open) door. There is also a wall terminal (100 Science to hack) next to the door that can be used. Then read all terminal entries and deactivate the robots without firing a shot or being caught by security robots without the correct security clearance.
The third keycard is obtained via a computer (75 Science to hack) on the second floor which makes it possible to print a third floor keycard. When done, the keycard is placed directly into inventory.
Regardless if you hack the computer to create a third floor keycard or loot the third floor keycard from the suitcase on the third floor the security robots will not recognize you as a legitimate person on the third floor unless you have Luck 7. You can deactivate the robots via the third floor Science 100 computer or you can kill the security robots one at a time without the other robots seeing it to avoid the alarm going off while you are looting the third floor. Even if you set off the alarm on the third floor it has no effect on the first or second floor robots.
The robots cannot be looted if they are deactivated.
The robots outside the facility and the tour guide robot will still be activated after deactivating the robots in the terminal.
PC If you hack the computer to create a third floor keycard or loot the third floor keycard from the suitcase on the third floor the security robots will not recognize you as a legitimate person on the third floor unless you have Luck 7.[verified]
Behind the scenes
The name of this quest is a play on the phrase "Axis Powers."