1. Download Reshade 3: https://reshade.me

2. Select Arkham Knight executable for Reshade installation (D3D11):

Executable located here: \steamapps\common\Batman Arkham Knight\Binaries\Win64\

3. Download shaders when prompted, only shader needed is LUT, but SMAA is recommended too (for better AA vs in-game version)

Make sure 'reshade-shaders' folder exists in the Win64 folder where BatmanAK.exe is located.

4. Download the file from NexusMods:
Extract the contents and copy reshade-shaders folder to the game directory. Overwrite if requested.

5. Launch the game, Reshade window should pop up. Enable LUT shader in Reshade window. The preset should be applied.
You can change Reshade to 'performance mode' in the settings tab for better performance. Additionally, you can disable in-game AA in favour of the SMAA shader in the Reshade window.

Pro Tip: You can adjust the LUT chroma amount to suit your liking. You can even bypass the '1.0' value cap by 'Ctrl+Clicking' the value and typing whatever value you want to (for example 1.2).