Tomb Raider I-III Remastered Starring Lara Croft

Done in TR3 - Crash Site.

This achievement is quite annoying to pull off, but especially during a Pistol Only run, thanks to the 90's AI of the soldier. The T-Rex takes ages to kill with pistols and opening the gate to get the soldier down to the lower ground risks getting him killed by both the red dino that spawns AND the T-Rex, so it's best to keep him "locked up" in the upper area until the fight is over.

Save regularly on a separate slot during the fight. Unlike previous TR games this T-Rex is extremely aggressive and will eat you (1 hit kill) if the game detects you're even a little close to its face. The moment you pick up the keys, sprint as fast as you can to the ramp that you slid down to get to this lower part of the area.

Facing the ramp, look to the right. There's a small crevice with a lever here. This is a safe place and it's close enough for the soldier to pick at it too (though he really doesn't do much)! You'll be able to safely shoot the T-Rex from here, only losing a little bit of health during the fight, but still save regularly in case the game's AI figures out what you're doing and eats either while you're pulling it back or perhaps eats you anyway.

Once you start getting very close to killing it (yay for a visible health bar!), save, and shoot with deliberate shots to see how many more it needs to die. You need to get its health down so that your very last pistol shot will kill it (it'll be an empty health bar at this point + 3 shots). Once it's at that point, put your pistols away and use camera mode to see where the solider is (LS + RS). Unfortunately he has a habit of running off to the back of the area, but keep luring the T-Rex towards you and at some point the AI will "catch" it and you'll start hearing his gunfire. It will take him a number of shots at the T-Rex to get the kill, but keep at it.

The achievement will unlock the moment the T-Rex dies.