The Awards are:
Head Shot - Shoot someone in the head.
Head Shot Heaven - 5 head shots in a row. (thanks to Borandi)
Great Shot - Kill someone from a distance.
Crack Shot - Same as 'Great Shot' but further away.
Snap Shot - Press to do a 180 degree turn and kill someone.
Gatecrasher - Break through a doorway that is boarded up, then kill someone.
Death Roll - Press to perform a roll, then kill someone when you come out of it.
Ric-O-Slay - Kill someone by bouncing a bullet off of a surface.
Penetrator - Kill someone by shooting through an object.
Multi-Kill - Kill 2 or more people with an explosion.
Last Bullet - Kill someone with last bullet in your magazine.

Select the very first level of Steel Mill. ('Pressed Into Action')

When you start, select your pistol and shoot at the wall/ground/air until you only have one bullet left. Peek around the corner and shoot the guy on the right in the head, giving you 'Last Bullet' and 'Head Shot'. Continue through the level as normal, shooting every enemy in the head till you have 'Head Shot Heaven'. Continue onto the metal walkways, if you go down the walkway on the far side, a guy at the end near the stairs will hide behind the metal bar. Shoot through that to get 'Penetrator'. When you come down the stairs, an enemy will come busting out of the door on the right. Shoot at the metal plate hanging opposite to the door. You may have to try a few different angles, but eventually, you'll get 'Rico-slay'. Perform a roll and kill the other guy to get 'Death Roll'.

Next, make your way into the area with the train and do 'Snap Shot'. On the walkway there will be two guys, taking one out will give you the 'Great Shot' award. The train has one wagon with two gates, smash through these and kill the guy at the other side, giving you 'Gate Crasher'. (If you don't get this, you'll have to restart.) Continue through to an open area which has two explosive gas tanks. There will be one guy running down the stairs they are positioned at and another guy that is jumping over the railing of the stairs. Kill these guys and the one sitting to the left. Do not move into the area until you've done this. After the area is clear, walk in and you will have two guys coming in from the left, throw a grenade and get them both in the blast radius, giving you the 'Multi-Kill Explosion' award.

Going through the gate, you will get into the final area of the level. Stay at the point of the gate and wait for the smoke of the explosions to clear. In the back of the space on the walkway there will be two enemies. Shoot the one on the right giving you 'Crack Shot'.