Strictly Business

Strictly Business is a side quest in Fallout 3 as well as an achievement/trophy.

Quick walkthrough

 * 1) Approach Paradise Falls.
 * 2) Get a slave collar and Mesmetron from Grouse.
 * 3) Enslave the people on Grouse's VIP list.
 * 4) Come back for a slave collar whenever you have to enslave another person.

Detailed walkthrough
As you try to get into the slaver compound of Paradise Falls, doorman Grouse will address you and tell you that you cannot enter Paradise Falls unless you have business there. He will offer to let you in only if you go and enslave select people from his "VIP list". You will be allowed into Paradise Falls after you have enslaved at least one VIP.

He tells you that his VIP list consists of four individuals that have mucked up slaver business and he wants them put down... or rather put away. These people are Flak of Rivet City, Susan Lancaster of Tenpenny Tower, Red of Big Town and Arkansas who hangs in Minefield. If Susan, Red, or Arkansas are dead before the quest is given, they will not appear on your list, and Grouse will allow you to enter Paradise Falls.

Slave hunting
Flak used to run with the the slavers of Paradise Falls but left without telling Eulogy. He can be found in the Rivet City Marketplace during the day and in his room on the upper deck at night. He is probably the most difficult VIP to capture. Sneaking into his room during the night meets the least amount of resistance.

Susan Lancaster also ran with the slavers but didn't pay the exit fee before fleeing to Tenpenny Tower. She is found on the third floor of Tenpenny Tower in her penthouse suite (at night). Simply shut the door, mez, and collar. If you enslave Susan while others are present, then the whole tower will be on alert and come after you with deadly force. Try and do it discreetly, or follow the note and affair scenario.

Red promised the slavers some things but didn't follow through with them. She can usually be found in her clinic in Big Town. If she's not there try walking around a bit and then enter her clinic again. If you did not complete the Big Trouble in Big Town quest yet, Red is captured by super mutants and held in the Germantown police HQ. You can simply enslave Red there, but it will prevent you from completing the Big Trouble in Big Town quest unless you rescue her from Paradise Falls later. It is possible that she gets killed by a super mutant attack after completing Big Trouble in Big Town and you will not have to enslave her.

Arkansas once took out a Paradise Falls slaver squad when they heading past Minefield and Eulogy Jones wants him to suffer. He is sniping from a ruined building on the edge of Minefield. Be careful as you make your way through the town, as land mines are scattered all over the town. Cars also will be shot at by Arkansas and can kill you. Once you get close enough to his nest, he cannot get a bead on you and try to make a run for it, surrendering. Simply mezz him here and take him to Paradise Falls.

Bugs

 * If you enslave and order a victim to go to Paradise Falls, and then die/reload a previous save, the character you've enslaved before you reloaded the save may appear in the Paradise Falls slave pen, without a slave collar on, and with all of the dialog options they normally had (for instance, you can still trade with Flak in the slave pen if he does not have a slave collar). Reloading the save will not fix this problem every time, so you may have to somehow get the target to come near you in the slave pen where you are able to Mesmerize and fit a collar onto the target. If Arkansas was the target, he will pull out his sniper rifle and begin shooting everyone around him.
 * When mezzing a person in V.A.T.S. with the Mysterious Stranger perk active, the Mysterious Stranger may appear. The Mysterious Stranger will look and move around, but no gun shots will be fired. If there is another enemy close by, however, the Stranger will shoot them instead.
 * You may be able to get paid two times for each of the VIP slaves you get. After getting paid the normal money when you reach Paradise Falls you can pickpocket a key to the slaves pen. Upon talking to all of the VIP slaves you captured and returning to Paradise Falls entry Grouse just repeats the speeches as if you just got the slaves and pay you again. You can repeat this glitch for an unlimited amount of caps.
 * If you enslave Flak, Shrapnel may disappear from Rivet City. He will return only once in a long while (every few days/weeks). He can be seen wandering the wastes and even in Paradise Falls likely looking for Flak. Apparently, Shrapnel's wandering after you enslave Flak is caused by an AI script that says the two should sleep near one another. Enslaving Flak thus causes Shrapnel to wander the wasteland trying to get to him.
 * If you enslave Red right after you freed her from the prison and fast travel to Paradise Falls, it will complete the task "bring back Red to Big Town" and "enslave Red from Big Town" at the same time, if Strictly Business and Big Trouble in Big Town are both quests in your Pip-Boy. However, after fast travel back to Big Town you can see Red on her way to Paradise Falls, you can remove her slave collar and then ask for your reward bringing her back to Big Town.