I got this the first time I tried it and never really came into any trouble until the final fight with the Darkness.
Your stats will be so far above 95% of the enemies you face the key thing is ensuring you have a couple of equipment cards to help you make swift progress through the traps and doors you face. In terms of combat I don't think I got hit more than once in the entire game.
It's key to remember the Darkness needs the laser gun you start with to die, so preserve your ammo on that at all costs.
I went through with a Chainsaw and another gun and that was more than enough to pile right through. The bonuses you get with the Chainsaw, coupled with the stats you get by playing on Easy, are more than enough to win all the combats you face.
Even with the right set of equipment you could end up losing once you face the Darkness as it comes down to a tough roll to win even with the laser gun. I had to roll twice and if I missed the last roll I'd have had no way to kill him, so there may be an element of luck in the end even with the bias of the stats by playing on Easy.
One other thing - the achievement is to beat the game - you can take a suicide jacket which would make the game a 'draw' as it kills you both - there's not much point in this so use your points to get something else.
In summary:
Get a Chainsaw
Another gun for ammo if you can
Save ammo on the laser gun for the end
Don't bother with a suicide jacket