This can be quite tricky, even on casual difficulty. I would suggest going for this on the first major boss encounter against Rajani. There is a save point just outside the boss fight. Whilst here, unequip all your good gear and equip all your starter gear. You will know which gear this is as it will all be worth 0 gold. Make doubly sure you are not equipping any rings or trinkets that come via the collectors edition DLC as these do void the achievement (they did for me anyway).
Once you are sure you have everything set as starter gear, fight the boss. It will heavily depend on which character you are using but some tips will work regardless. Firstly, try and avoid damage as much as possible. Even on casual, she can strip a full health bar off you in your crappy gear very fast. Abuse your healing ability, it will save you in this fight.
First form really just needs you to dodge when she hurls the spear at you and maintain a distance as much as possible to avoid her spinning attack.
Second form is the trickier part (at least I found it to be). Trick here is to deal as much damage as possible to the boss. When you do enough, she will teleport away from you and spawn blue fire portals on the ground. DO NOT stand in these as they will tick your life away very fast. Also, be wary of the boss shooting blue fire at you. When you see this, dodge away immediately and make sure not to stand still. If it does hit you, it will ignite the floor beneath you and will kill you in one shot.
It will also be easier playing co-op as the computer can sometimes take an age to revive you. In the second form of this boss fight, that will spell defeat.
Hopefully, using these tips, you will get her down fairly quickly. When I did the achievement I used Katarina and I must say, her ranged attacks helped a great deal.
I can also confirm thanks to several people that your partner can wear any gear they like as long as you only have on your starter gear. Also to confirm, this boss is the first (and easiest) chance you get at this achievement as the mini bosses don't count.