The other guide doesn't explain very well what you need to do here. A bandolier is an ammo belt.
Playing through the campaign you will earn diamonds for completing missions and locating the cases around the map. During the tutorial missions you will unlock the weapon shops. When you have approx 15 diamonds go to the weapon shop and use the computer. You can change pages by pressing RB. Buy the Makarov pistol (first page), the accuracy and reliability upgrades (second page) and then the Pistol Belt (third page). This will unlock the achievement. If you don't want to keep these parts/upgrades you can easily save (at the box on the wall in the shop) before purchasing and then revert to your saved game.