You need to fully upgrade all of your weapons by finding all the "Power to the People" stations throughout the game. Make sure you do not kill Sander Cohen until you access his room in Olympus Heights or you will forfeit this achievement. Here are the locations:

Neptunes bounty - After defeating Peach Wilkins and after getting back all your weapons, youll head down the stairs and walk right into it.

Arcadia - If you head towards farmers market, you will enter a place called "Tree Farm" (this will pop up at the bottom of your screen) and you'll go up a small set of stairs, right below the huge green "Farmers Market" sign above these stairs and directly left of the sign is the weapon upgrade station.

Farmers market - Go to Worley Winery, head down the first set of stairs, turn left and on your second right you'll see another set of stairs. Go down those and head straight into the water and you'll see the weapon station to your right.

Fort Frolic - On the first floor head to the southern mall (Southern Mall will pop up at the bottom of your screen) and there is a vending machine outside of this open area. Follow this path to "Le Marquios D'epoque" store. Once inside turn right and head downstairs, make your first left at the bottom of the stairs. You'll see the weapon upgrade station inside this hallway.

Fort Frolic - Head to Posidon Plaza, then pass through the frozen area, turn right and head staight to "Sinclair Spirits." In order to open the door inside Sinclair Spirits, hit the switch behind the bar. The switch should be right next to the cash register. Once you hit the switch, head to the door behind the water thats falling from the roof. If you still cant find it, it is to the right of the jukebox. Once inside, head downstairs and turn left for the weapon upgrade station.

Hephaestus - This one is in front of the gatherers garden machine which is to the right of "Heat Loss Monitoring".

Hephaestus - Head to the office of supervisor Kyburz which is downstairs in "The Workshops." This door is guarded by two turrets. Inside this room, all the way back and to your left is this weapon upgrade station.

Olympus heights - Head towards the main apartment building called Mercury Suites and you'll see at the center are some stairs with an elevator leading up to the 2nd and 3rd floors. On the opposite side of the elevator is the Weapon Upgrade station.

Olympus heights - Sander Cohen's apartment is to the left of the previous weapon upgrade station (if you are facing it). You should hear Sander Cohen on your radio once you enter his apartment, so long as you did not kill him earlier. He'll tell you not to disturb the two dancing houdini splicers. Kill the spilcers and you'll be able to enter his room. His room is the first door to your right when you enter the apartment. As soon as the door opens, you go up some stairs, at the top of the stairs and to the left is a weapon upgrade station.

Apollo square - Head to Fontaine's Home for the Poor, head all the way up to the final floor and enter Atlas's Headquarters. Inside you will find stairs leading down to the weapon upgrade station

Point Prometheus - In the main open area, there should be a fallen big daddy infront of a vita-chamber. The weapon upgrade station will be right next to the dead big daddy.

Point Prometheus - When heading to "optimizied eugenics" for the big daddy voicebox, go inside the door labeled "eugenic analysis" you'll know you are in the right room when you get attacked by two turrets. The upgrade machine will be at the back of the room to your left

Check this thread for maps.

Some of these are received by research, some are found hidden in the levels and some are given as gifts by the Little Sisters. You need to save every Little Sister to get this achievement, seeing as they give you a tonic as a gift at the end of the game.

Check this thread for all the locations.