I have finished Atlas Fallen on the highest difficulty in NG+. The interesting part is that the tools available (the weapon upgrades, new armour sets, and the more powerful Essence Stones) effectively offset it - while the bosses could 1-shoot me, I also was almost instantly and constantly at high Momentum (which additionally meant higher damage to me) and able to use the Shatter attacks with a lot of i-frames repeatedly. The longer battles were somewhat challenging, especially as the screen was getting more "noise" (from the weapon particles to the number of opponents), but, overall, it was easier than the first playthrough.
The only issue is one of the randomly appearing battles with various modifiers. The foes to be faced vary, but the reward progression is static and carries over between the NG cycles. The thing there is that it is not hard to get hit once and the battle despawns after that. I assume, if I reloaded, the same battle would have been accessible at the same spot, but I have not tried. The regular random battles have an auto-save nearby and the main story ones can be restarted from the start of the encounter which is incredibly convenient.
I am satisfied with the experience and might try replaying it in a few years.
On a random note, the NG+ armour sets look much better than the NG ones. They are more detailed and more fitting.