To get to the weapon you need to navigate the Twilight Cathedral. There will be chests you can't get to until you obtain the Crossblade and you will need to go underground to get it. But don't worry, you'll be able to go back topside soon enough.
When you first get in the Twilight Cathedral you'll see some cool fight scenes from the aftermath of your Gryphon ride. But your main objective is getting past that hanging maw holding the statue in midair. Here you'll find many blue swords on small dais just waiting for your gauntleted hands to grab. These swords will replace your own until you find a use for them, which apparently is to hand them over to the waiting arms of empty-handed angel statues. Once the statue literally gets a hold of the sword, it will turn the blue light red and unlock the door close to it.
You'll need to repeat this process throughout the cathedral. As well as blow up red crystals. These giant red crystals block your way to your objectives, be it gate levers or treasure chests. The way to get past them is to blow them up with a well-placed bomb. Many crystals would already have the bomb attached. So you could just Earthcall them to blow up by vibration, especially useful for one on the balcony of the wing to the right. (NOTE: You can use the Crossblade later, but I recommend getting the maps on the balcony before going down to aid in your navigation, your choice.)
Two enemies, besides the hanging maw, will give you a hard time. Armored guards will often be waiting for you in the sword chambers. The way to beat one of these monstrosities is to chip at his armor (helmet, chestpiece, right gauntlet, left gauntlet) until his top's bare and he kneels. This can take quite a few hits and his own strikes are powerful, in Apocalyptic takes half a life bar from me with a direct hit. Jump over him when he swings or run to the side if you can. Hit him in the air or right after he swings from the back. He'll eventually go down.
And the other hard foe is actually after you get the weapon, so let's first get to the goods.
Throw a bomb at the hanging maw, clicking and then moving right stick to aim until you get a target on it and RT to throw. The maw will retract and let go of the statue, letting it crash through the floor to open up the lower levels for you.
After some battles with undead soldiers, you'll reach an antechamber you have to jump down into that holds a box. Open the box to receive your weapon!
Though the achievement will pop up right after you get the weapon, so will many enemies, so here's some tips to survive it.
The lava bats (yes, lava bats) won't be hard. You just need to get them close to you. Back away and do as directed with your Crossblade. Knock them down on the ground so you can hack at them. OR you can do as you do with the other bats. Ride them and gut them. Have fun.
Remember the second enemy I promised would be a toughie? Well, here he comes to wreck the day, right after the lava bats. An ugly puss-filled brute that spews poison at you and swipes you for major damage. Keep away from his claws and throw that new weapon charged to interrupt his poison attacks. After you press B to incapacitate him, be sure to get to safe distance before finishing him with the Crossblade or he'll explode in a cloud of poisonous gas on you. Once you survive him you have a better chance of moving on.
Congrats! Now good luck fighting your way out. ;)