This achievement is for beating the game on Classic Mode. This is under New Game+ once you beat the campaign for the first time. You start completely anew with no items from your previous save.
The difficulty is automatically set for hard (which when you beat the game on impossible and go to hard afterwards, doesn't seem all that terribly hard)
In this game mode, the difference from the standard campaign is that only classic weapons are available for crafting (i.e no acid attachments, or anything that was introduced in Deadspace 3 to the player)
You begin with a plasma cutter which i suggest using throughout the campaign as your main (and if you so chose) only weapon. The first chance you get you should upgrade the plasma cutter with 4 +1 Damage +1 Rate of Fire circuits on the top circuit board and 4 +1 Reload circuits on the bottom.
The bottom circuit board on the plasma cutter seems to be only effected by reload circuits, so putting anything else there is just a waste. eventually you should aim to have damage full and pile everything else that you can (on the top circuit board) to rate of fire.
With still a fairly sizable chunk of the campaign remaining. it is possible to collect a full set of a type of artifact which unlocks certain circuits that you can craft and then use for the rest of the campaign. I myself used the +3 Rate of fire +2 Damage circuits on my gun's top board and it was essentially a hand cannon that shoots at a ridiculous rate. (As long as you have a good amount of ammo) you don't really even need to be a good shot. Just unload and watch enemies just drop before your eyes.
Co-Op is disabled for this game mode and therefore can only be completed solo. (If you're waiting for your friend to get the game after you've beaten it already so you can play Co-Op together, but you still want to play then classic is the way to go because you can't play Co-Op on it anyways)
Finishing the Classic Mode campaign unlocks the "Devil's Horns" which is a weapon that is a foam finger (like what you'd see at a sports event) Although in Deadspace 2 you could also unlock a similar (if not the same) weapon and it had unlimited ammo and killed everything in 1-2 shots. I cannot yet confirm whether the gun does actually still have unlimited ammo and is as powerful. I will when I complete this difficulty though.
Remember...aim for the limbs ;P Good luck.
*EDIT* Ricky Horror commented that "The Devil's Horn's uses ammo. And yes, (it) is very powerful. All stats on it are completely maxed except for rate of fire."