Before we start, you're gonna need Reshade installed on this game. You can get the latest version here: https://reshade.me for free.
This guide will not explain how to install Reshade or its filters, since its a pretty simple thing to do and there's tons of guides that explain how to do that already.

1: Type "Registry Editor" in the Windows search bar and open it.
2: Double click on HKEY_CURRENT_USER. Double click on SOFTWARE. Double click on Crystal Dynamics. Double click on Tomb Raider: Underworld. Finally, double click on Graphics.
3: Once you're in the Graphics folder, look for "EnableDepthOfField". Double click on it and change the value from 0 to 1.
4: Close Registry Editor.

Inside the game:
1: Open the Reshade tab and look for DisplayDepth in the Home tab. Activate it.
2: After that, go to the Addons tab and activate Copy Depth Buffers Before Clear Operation.
3: Now go back to the Home tab. Click on Edit global preprocessor definitions. Change the RESHADE_DEPTH_INPUT_IS_REVERSED value from 1 to 0. It should look like this:
If you don't have any values to change, click on "+" and paste this:
RESHADE_DEPTH_INPUT_IS_REVERSED
Then make sure to put 0 on its value :)
4: This is it! Now disable DisplayDepth and enable MXAO.

IMPORTANT: you need to disable Antialiasing in-game in order for MXAO to work, otherwise it won't do anything.
This also enables effects like ADOF or CinematicDOF.
Enjoy! :)

Here's a list of some of my most used filters not just for this game, but in other games too.
FXAA + LumaSharpen is a great combination. Improves sharpness and makes up for disabling Antialiasing
Vibrance/Colourfulness are always nice for a little bit more color.
Curves/Levels are both great to add some contrast to the game.
Border is just the cinematic border you can see in some of the screenshots shown in this guide. It's purely for a cool cinematographic look.
Vignette always adds a nice little feel to the game.
DOF effects (ADOF, CinematicDof, MagicDof, etc) look great specially in cutscenes and virtual photography.
Ambient Oclussion effects (MXAO, PPFXSSDO, etc) look great in older games like this one.
NiceGuy Lighting can be used to either add GI/AO or Specular Reflections.
SSR is pretty much only good for Virtual Photography. Specially in rainy places since it creates reflections on the floor.
And I probably forgot some but you can always try filters yourself and find out what you like ;)

Here's some screenshots!






Don't be afraid to ask anything, and please let me know if it worked for you :)