Kill the turtle in the tutorial area.

This is actually pretty easy, but also easy to miss. So, first enter the tutorial then when you enter the first turtle you see is the one you need to kill and at first glance it might seem as if he is unkillable, but just keep unloading on him and he will eventually die then you will get the achievement.

Beat the game using Ass/Ace (you can use warps so I don't recommend starting from the beginning).

Edited a bit to fit with update 4.

Weapons - So, first you need to select guns and I suggest a Sniper Rifle and Highmag (the Highmag may be hard to come by and if that is the case just use another pistol. The reason for these is the Sniper Rifle does high damage and you don't need to be right on someone to hit them, but be aware that you will miss some shots because Ass/Ace doesn't have high accuracy and i've selected the Highmag because of fire rate, range, and that it doesn't take up heavy ammo, but feel free to use what you want (though, you should consider range when picking another gun).

Relics - On my run I used Extra Shield / Shield Regeneration / Extra Damage, but Maximum Health / Extra Shield / Extra Damage is good as-well. Please don't let this discourage you from using a Relic you would like to use, but keep survival in mind.

Strategy - Now what you want to avoid as if your life depends on it (it does) are explosives (grenades and rockets) because grenades will take out all of your shield and a rocket will take away your shield and a majority of your health, but only if you're using the Relics Mamimum Health or Extra Shield. Also, just one of these Relics prevents death by grenade and both prevents death by rocket launcher. I would also like to add that you should be careful, don't rush in because you will die you ARE the weakest character and you should also allow your shield to recharge whenever it depletes.

Boss Fight - Again just avoid explosives and whenever the enemys spawn you should kill all of them because if they start to build up or overwhelm you then you're most likely going to die.