Assuming you've followed the guide to this point, you have at least two achievements left, and possibly more, but you've finished your first playthrough.
If you have not yet run Dosan's Story, the side mission accessible from the chapter select screen, do so before beginning your second run (see the main walkthrough for details on the achievements you should get there). Once that's done, start a New Game+ run. Take note you can skip cutscenes. When you start the first level, you'll get the upgrade screen. If you got every seal, scroll, and star in your first playthrough, you'll have just enough points to purchase anything you didn't already:
Earn all of the upgrades.
You definitely have your New Game + achievement left. You may have up to four others I haven't mentioned yet, depending on your playstyle. The reason I didn't mention these earlier? Two reasons. First, you may just get them naturally. Second, if you don't, the best place to get them is in levels before you unlock the skills you need; rather than backtrack, it's just more efficient to get them on your second playthrough.
Some notes on your NG+ play: I always recommend the Path of the Mark costume for the Serenity skill unless you are going for some specific achievement that prevents you from using it, or unless you are just having fun. (Path of Nightmares and either terror darts or ravenous insects is great for the sheer pleasure of scaring guards.) Serenity in the early levels reduces most of them to a joke - you can speed through these levels in three or four minutes each in some cases. Up until level 11, where the levels are really designed for Serenity, having the ability is simply game-breaking. If you're up for speed, it's essential to your buildout. You can finish the game in about 4 to 5 hours.
In NG+ play, you do not get the sound indicators or any visual indicators of enemies' hearing range and such. You'll also be killed incredibly quickly in a fight, and the enemies are tougher to kill in melee battle.
One achievement you'll likely need if you followed the main walkthrough requires dusk moths, and is available in the first level. Build out with the dusk moths (and Path of Wisdom if you don't have What Could Have Been) for your first NG+ level. When you get to the light that you can't put out with a dart (Ora will say "We need him to turn around," and there's a gong just past him for you to ring), use the moths on the light above him. That will get you Couldn't Do That Before:
If you finish the level with the Path of Wisdom, you'll get What Could Have Been
, if you didn't already have it.
From the second level on, I recommend you build out with the terror darts and Serenity until you get the three terror achievements (listed below). After that, Serenity and whatever else you want. I like the insects, but it really doesn't matter. Serenity allows you to skip entire puzzles, and even if you're spotted you can jump clear across the screen and start running.
The sole exception is if you didn't get the Dosan's Story-related achievements on your first runthrough, in which case you'll need to make a stop at level nine for those achievements (see below).
The best place for Unstable Footing is in the second level. When you get to Floor 19, make your way all the way to the left, killing all the guards on the way. Open the leftmost door to find a guard standing there outside on a smoke break. One terror dart sends him plummeting to his death:
Gallows and Oni are best tackled at the beginning of the third level. There are two guards, first thing. Drop down, kill the first, and while dragging his body to the left, target the left grapple point and hit RB to hang him from it (the other grapple point won't allow this). Then walk just over halfway between there and the next guard before sprinting back to the hiding spot (a trashcan directly under the hanged guard). The second guard should come investigate the noise you made, see his partner strung up, and freak out. He'll probably shoot you by sheer accident as he wets himself. Reset the checkpoint and do this again until you've done it five times across both playthroughs:
Terrify a guard with a hanging stealth kill five times.
At this point, you probably already have the last terror achievement, which you get from terrorizing 10 guards. If you don't, just start using your terror darts as you go through the level until it pops:
Terrorize 10 guards.
If you're not going for the Dosan's Story-related achievements here, you're free. Use whatever tools you want, whatever method you want, to finish your NG+ playthrough. It will probably take around five hours, assuming you burn through using Serenity. While it's allegedly harder than your first playthrough, the fact that you don't care about alarms, points, scrolls, or seals make it a cakewalk. Plus, as noted, Serenity makes the first ten levels a bit of a joke.
If you didn't get the Dosan's Story achievements already, however, you have a brief stop at level nine. When you get there, equip the moths and the fungus. When you get to the first keyholder, you can use the fungus on him, which will make the other two guards turn around and investigate to give you Cordyceps. Get the key and keep going, almost immediately you'll come across an elite with a dog. Hit the elite with the moths (the dog too, if you want) and take him out for The Humble Moth. You can either continue through the level or restart it so you can equip Serenity. Either way, finish up the game in your choice of styles from here out.
When you're done, bask in the glory of your completed game:
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