Take the last elevator to confront Sinjin. From here there's several options:

Stealth - A stealth approach to this encounter is surprisingly dangerous. If Sinjin detects the Sole Survivor at any time, then stealth kicks back in, he will yell "You're not walking away from this!", kill Kent, then turn hostile. If Sinjin is killed with a stealth headshot, the unnamed raiders will turn and kill Kent, starting with the one to the left of the elevator. Avery is the only person not scripted to kill Kent, but commonly strafes behind him while shooting, inadvertently killing him in the process.
It is still entirely possible to kill Sinjin and the two raiders before they kill Kent, although their reaction time makes it effectively impossible without using Jet and a strong and fast weapon.
Intimidation - Speak as the Shroud and Sinjin's bodyguards will run. The same thing can be accomplished with a difficult speech check for more XP. However this method will cause Sinjin to immediately target Kent. If playing on survival difficulty it could be difficult for some characters to defeat Sinjin before he has a chance to kill Kent.
Pacify - For those with a high Charisma and the appropriate perk, it is possible to pacify Sinjin and his bodyguards on exiting the elevator, before the dialogue options appear. After choosing option 1 or 2 above they will not target Kent, especially if turning the bodyguards against each other. This leaves Sinjin as a target.
Persuade - A difficult persuasion check can make Sinjin target the player instead of Kent.
Beg - Sinjin can be asked to spare Kent, but he just kills Kent immediately.
Kill Kent - Upon exiting the elevator, one can kill Kent before talking to Sinjin. This will trigger unique dialogue where Sinjin and his gang panic. Wearing Shroud's costume will further allow another unique dialogue where the player can turn Sinjin's gang to their side.
Silver Shroud - Speak to Sinjin three times in a row as the Silver Shroud and then kill him before he finishes his dialogue after Avery comments that the Silver Shroud is real. This will cause all the raiders (including Avery) to run away and become pacified. If one attempts to talk to Avery or the other two raiders after, they will say they did not want to work for Sinjin anyway.