Tomb Raider I-III Remastered Starring Lara Croft

Done in TR2.

Level skip voids the achievement. Unsure about weapon cheat but... You're only using pistols so there's no reason to do it.

This is achieved by completing the game only firing pistols. I don't know whether simply getting another gun out will break the achievement, whether firing at nothing voids it, or if you need to actually fire another weapon at an enemy for it to count. Just avoid tempting fate and if you fire another weapon for whatever reason, just load your last save.

You can pick up other weapons without voiding the achievement, but I recommend to never equip them.

As Corax discovered you can also kill enemies with vehicles just fine [I]ONLY[/I] by running over them. HerrKätzchen confirmed, you must NOT shoot from the vehicles. Thankfully in Tomb Raider 2, the only vehicle you can shoot from is the black snowmobile. If you fire the guns for whatever reason, load your last save.

On the subject of the Tibettan chapter, I highly recommend on your Pistol Only run to also go for the "Complete Tibettan Foothills without getting on the snowmobile" and "Make all stalactite traps fall without getting hurt" achievements. I also recommend NOT going for the "Ensure all monks stay alive" in the Barkham Monetary. Of course it's up to you.

Also keep in mind that stages where you'll come across enemies underwater, you will NOT be able to use the harpoon gun. So get through underwater sections with enemies in them quickly and either find ground to shoot them with pistols, or avoid them as much as possible.

The achievement will unlock when the completed level stats appear for The Dragon's Lair (as the only gun available in Home Sweet Home is a shotgun - thankfully the devs considered this :)).