This achievement is really quite easy (and very fun!). Once you've completed the game the first time you'll unlock New Game Plus mode, in which you start the entire game again but retain your character level, weapons, and upgrades. This means that you don't have to re-earn virtually anything and you can really speed through the game for this achievement. So New Game Plus is super easy, but it could get tedious if you pick slow weapons.
In starting the game again, I would HIGHLY suggest using a fully upgraded Scrap Musket with the damage-increasing upgrades selected because it makes very short work of virtually everything in the first half of the game. I would also recommend using the Cael Hammer because the charge-up slam can still be very handy even when you're blasting your way through New Game Plus. For a special ability, I used Final Warning for the Scrap Musket because it is an excellent crowd-control ability for those few times that you get swarmed.
I used these weapons for nearly the entire playthrough of New Game Plus (though I used the Mortar for the last level). Even the tougher Ura enemies didn't stand a chance against my Musket, making combat simple and fast. In fact, I was barely ever injured and needed only about 7 or 8 health potions in the entire game.
It is easy to complete your entire New Game Plus playthrough in about 2.5 hours, maybe a bit less. Skipping all weapon Proving Grounds helps speeds things up, as well as not bothering to collect everything. And when you get to the end of the game for the second time, be sure to make the opposite decision than what you made the first time so that you can get the other end-game achievement.