This Achievement unlocks upon completion of Act 7 of the story when played on The Killer difficulty. The game must be completed on Assassin difficulty before The Killer difficulty is made available.
The initial section of this stage is pretty straight forward run-and-gun with cover. Always go for headshots on the dudes with shotguns, and don't waste ammo on the hooded psychos that run at you with their knives. They're not that hard to beat in close quarters, since the button press is always "B". Just wait for them to engage, hammer on the B button, then return to cover when they're dead. Nobody will shoot you during the melee.
Once you kill the cable car operator, it's more of the same as you fight your way back to the cable car. Take your time and use the tools you've learned along the way.
Blast through the next compound, using curved bullets to take out enemies in doorways, and watch for the mines on the floor. Take them out with a well-placed shot from a safe distance.
When you reach the boss battle against Araña, stay in cover behind the two columns in the center of the stage. Keep in mind that they will deteriorate with gunfire, so be quick and accurate when you pop out to shoot enemies. Don't try to follow all three sides of the room. If you stay in cover, you'll be fine. Just pan and scan from the center to the right side watching for enemies to appear outside the window, or for Araña to drop down from above.
If it's a normal enemy, pop out, cap him a couple times and drop back into cover. This will help fill your adrenaline meter as well as keep you alive. When Araña drops down, dash to another piece of cover using the A+Y combo that slows down the action. Unload as many shots into her head as you can while in slo-mo, and repeat this tactic until she's dead.
The stage still isn't over yet though... you'll need to fight your way underground until you reach Cross' tomb. The enemies get a little tougher here, but you won't have to face another boss once you reach the end. Once you've found the tomb and the cinematics play, you'll unlock the Achievement.