Cario Station is just the tutorial level to get a hang of the basics. You can get this achievement on any difficulty setting.
You'll begin this mission as Master Chief who's being scolded for not looking after his equipment. This is the time that you'll be introduced to either the default or inverted control scheme. Choose whichever one feels right to you, it really doesn't matter. You'll also be introduced to the shield system. Your shield is located directly above your radar. It's straight-forward: getting hit will take your shield down. If your shield is gone (check the bottom left-hand corner, it will be flashing red) then take cover until it recharges. If you don't a few extra hits will kill you. You guys are probably intimately familiar with this, but just in case you weren't now you know.
Once the action has started and you have followed Johnson you should end up with a Battle Rifle and an SMG. There should then be a door that the Covenant are cutting through. If you shoot out the glass above the door you should be able to use the object around you to hop above it. When the Covenant burst through they will run straight allowing you to shoot them from behind or assassinate them. I suggest assassinating the Elite and then picking off the grunts. At this point it would be a good idea to switch your SMG with one of the Grunt's Plasma Pistols as it's incredibly helpful to charge a shot to take down the Elite's shield and then kill them with a single head-shot from the Battle Rifle.
The rest of the mission is pretty straight forward. Keep up the Plasma Pistol and BR combo and the Elites shouldn't be too much of a problem, The only time you should have any other weapon is when the Drones appear, in which it would be wise to switch back to an SMG (Bug-spray). An SMG should be located to your right when entering the room with the Drones.
The last part of the mission is a room full of Elites. When all the Elites are dead the mission will end and Chief will
With a few well placed grenades and the Plasma Pistol/BR combo this room should be pretty easy. Just don't rush forward as the Elites can kill you pretty fast.
While this mission can be completed with any combination of weapons, the Plasma Pistol and BR combo will make the heroic and legendary difficultly settings much more bearable.
EDIT: You cannot get the achievement if you have any x0.00 skulls as they technically make gameplay easier. Thanks to Teh Author for pointing this out down in the comments.
If you beat the par time of 15 minutes you will also get: