Library Of Ruina

First off, I would highly recommend not doing this until you get Roland's unique page, which is the 2nd fight after Impuritis. You might make it work without it, but this is what I did.

Your 4 partners should all be equipped with Rabbit Team Soldiers, with the full battery of first turn power passives (+3, +2, +1 power 1st turn) and Noah's page for extra ranged damage.

The deckbuilds will be simple. 3x Indiscriminate Shots, 3 x Take The Shot, 3 x Target Spotted.

You can't do much with Roland, but you can add Passives. I had Myo's Promise & Meat Gear along with The Red Mist's "The Strongest" and Mars' extra stagger on higher speed. Hit hard hit fast.

At that stage, your goal is to give the Purple Tear a machine gun welcome and just whittle her down before she can breathe. She'll teleport to random team midway through, I ended up getting a floor of dopes so I didn't scratch her but you might get lucky. Luckily, upon her return, your +6 powerups on your shooters re-apply. Plus, on your 2nd run 1st turn with the rabbit squad, you might want to prioritize Target Spotted over Take The Shot, as you want lots of feebles on the Purple Tear so Roland can sneak those last few points in.

Once you get her in range, try to be judicious of the damage you do, as I believe Roland has to be the one to land the killing blow. I somehow timed the end of her first turn back at 8 health, so I was able to just send him in for the kill alone on the first try. The "Lies" emotion page is quite good to throw on Roland if it pops up for you early on, as his lower cost moves all mostly have "This cost can't be changed" on them so it really just makes your expensive stuff cheaper and will help for the final push that turn you need to slay her.

In general, if you're having trouble w/the Purple Tear regardless of this achievement, this strategy couples best with Binah and her Fairy abilities. That's what got me through her on the story progression side.