assuming you don't want to cheat for the achievement:
You'll be wanting to look out for the Nuka-Cola Quantum bottles from the moment you start the game. There are well over a hundred of them, and you can find at least one pretty much everywhere you go. You will need 30 bottles of Nuka-Cola Quantum total. Keep an eye out for a purplish-blue glowing soda bottle wherever you go and make sure you don't use them or sell them. The girl who wants them lives in a two-house settlement in the southwest corner of the map.
A few locations where you can find multiple bottles:
- Nuka-Cola Machines - Every time you open one of these for the first time there's a random chance they'll have a Quantum in them.
- Eulogy's Pad in Paradise Falls - There are several stashed near the staircase in crates.
- Nuka-Cola Plant - located near the southern border of the map, near the center. There's a conveyor belt you can activate. You can get a few bottles from it before it breaks down.
- Nuka-Cola Truck south of Old Olney (northeast corner, east of Vault 92). There's an abandoned Nuka-Cola Truck with several bottles inside.
This a good achievement to work on while you're exploring for your 100 locations, 50 terminals, and 50 locks. Just check all the markers you run into on your map and search each location...most places have at least one terminal, lock, and Quantum.
UPDATE:
When you come back with the bottles the man outside will try to buy them from you so he can get in god favor with the girl. Keep in mind here that you can only get the Nuka Cola Grenade schematic by giving them to the girl. Also, all 30 Quantums have to go to one NPC, meaning you can't give one 10 and the other 20 to complete the quest. Some people give the guy 29 and the girl 30 so that they can get a ton of caps but still get the schematic.
Broken Steel, the third DLC expansion for Fallout 3, has added another way to get this achievement. If you have at least a science skill of 70 when you hit level 22 or higher, you'll have access to the Quantum Mechanic perk. This perk allows you to turn 10 Nuka Colas into one Nuka Cola Quantum, thus speeding up your progress with this quest. It does not, however, work on the Ice Cold Nuka Colas that you get from your machine. You MUST have the Broken Steel expansion to raise your level above 20 and gain access to this perk.