Tomb Raider I-III Remastered Starring Lara Croft

Towards the end of Lost City of Tinnos, after the room with the entrance to the 4 elemental rooms, you will arrive in a big square room with entrances on all sides. You will be attacked right away by a single mutant as soon as you enter.
The other 2 arrive a bit later.
To get this achievement, you must not be hurt by any of the mutants' attacks and kill them with only the pistols.

For the first mutant, simply start shooting immediately and jumb on the sides continuously before he gets to you. You should be able to avoid all attacks and kill him.

To trigger the other two mutants, you will need to approach the center of the room. As soon as you do, get back towards the entrance of the room and get up on the ladder just next to it. The mutants take some time to actually enter the room so you should have time to climb.

As soon as you are up, get next to the wall and CROUCH, as the mutants won't shoot you that way. You can shoot them whil crouched though, so it is then just a matter of time, shoot them while they pass below and the achievement will unlock as soon as they are both dead!

Here is a video where you can see where I crouched to be able to shoot the enemies: https://www.xbox.com/play/media/ndSGtbTf6H