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https://screenrant.com/metal-gear-solid-defeat-psycho-mantis-pc-controller/

Full article is below:
In the original Metal Gear Solid, Psycho Mantis is a telepath who can read Solid Snake’s thoughts. This means he can predict the player’s movements and cannot be harmed by attacks, as he will instantly evade them. In order to defeat Psycho Mantis, the player needs to switch their controller to the second player port. This will prevent Psycho Mantis from reading Snake’s mind. This same tactic is used for the PS2 version of Metal Gear Solid, but people playing it on PS3 will need to change controller ports through the menu. The PC version of Metal Gear Solid is on a system without controller ports, so the secret to defeating Psycho Mantis has changed once more.

Controller & Keyboard:

This is the most likely situation that players will find themselves in. If a controller is used at the start of the fight, then Psycho Mantis will evade all of Snake’s attacks and predict his movements. Campbell can tell the player that the keyboard is the way to hurt him. The player needs to switch to controlling Snake with the keyboard to harm Psycho Mantis. Any attacks performed while controlling Snake with a controller will result in Psycho Mantis predicting them.

Only Keyboard:

The people who insist on playing Metal Gear Solid without a keyboard will have the easiest time of all. If the player doesn’t own a controller and attempts the Psycho Mantis fight, then he instantly cannot read their mind and Snake can damage him from the start of the battle. The battle then becomes ridiculously easy.

Only Controller:

The people with a broken keyboard are out of luck. Psycho Mantis can only be harmed by keyboard controls and Campbell will just tell the player to switch to keyboard, even if one isn’t connected to the system. It’s assumed that all of the people playing Metal Gear Solid on PC will have access to a keyboard, so the devs can’t be blamed too much for this as an oversight.
It's not true that you're "out of luck" without keyboard, usually, after Campbell tells you to use the keyboard and you die again, you can call Campbell again and he will tell you how to defeat Mantis without switching to keyboard (the statue trick). In addition, in the PC version, it is not too hard to defeat Mantis without switching and without shooting the statues.
I found out that the game can't detect a controller plugged in after the game has started. So I just save before the fight, turn the game off, unplug the controller, turn the game on, plug the controller in and just use some keyboard mapping profile to keep using my pad for the fight.