Use this guide if you have severe input lag when aiming with a Mouse because of the forced 60fps lock. This guide does not outright fix the game's physics being tied to the framerate. Bethesda fixed it in Fallout 76 but not in Fallout 4 for some reason. Even on the next generation update didn't fixed it but broke the game even more.

Based on this reddit post inspired me to make one: https://www.reddit.com/r/fo4/comments/4udr25/pc_is_it_possible_run_the_game_at_120_fps_without/

Applications you need:
*MSI Afterburner
*RivaTunerStatisticServer (Comes along with MSI Afterburner when installing it)

Step 1 - Remove Forced V-sync through INI File

1.) Go to the directory where the INI file for Fallout 4 is located:

"C:\Users\[YourPC]\Documents\My Games\Fallout4"

2.) Open Fallout4Prefs.ini
3.) Find the INI Parameter called "iPresentInterval=1"
4.) Set the Value from 1 to 0 --> "IPresentInterval=0" (This will remove the 60fps lock)
5.) Once you set it, save the INI file and Go to Properties of the same INI file and set the Attributes and Check the box called: "Read-Only". So the settings won't be modified by the game's splash screen Graphics options.

(Be sure to set all Graphics settings however you want your game looks. Because I noticed that clicking the Options on the Fallout 4 splash screen will automatically revert the V-sync to On even by not clicking the save button for the Graphics Options. Even with the Read-Only check box was applied to that same INI File.)

Step 2 - Use RivaTunerStatisticServer to cap the framerate to 120fps

(RivaTunerStatisticServer is part of the MSI Afterburner app as a system monitoring tool and a GPU Overclocking utility. Make sure both applications are opened in order for this to work.)

1.) RivaTunerStatisticServer app is located minimized in the Hidden Icons on the Taskbar. Open It.
2.) Select "Add" and get the Executable file of Fallout 4 on wherever it is installed on your PC. To find out where Fallout 4 is installed on your PC: (Skip to number 3 if you know where you installed it.)

2.1) Go to Fallout 4 library page and go to the gear icon called "Manage" and click "Properties". Then go to the "Installed Files" and select "Browse".
2.2.) Another Window will be opened and it will show you where Fallout 4 is installed.

3.) After selecting "Add", select the "Fallout4.exe".
4.) After selecting it, click the "Fallout4.exe" on the black box and set the Framerate limit to 120.
5.) Do not Close the app but only minimize it.

Enjoy!

I am aware that there are Mods that fixes High FPS = Faster Animation problem. Even some that enhances performances and the stability of the game with Unofficial patches or basically makes the game better than intended. This is just another way to do it if you don't prefer doing it with Mods or playing the game with Achievements because it disables it when Mods are detected. (There is also a Mod that re-enables achievements if you had Mods installed.)