This is a video showing you how to obtain the achievement on NG++ with the axe called the Between. This dropped using the Fire magic school in the DLC to defeat the Keeper. I obtained the achievement on an earlier run, so it not shown unlocking.
At NG++ any damage taken was an instakill, except fire, for this reason I have limited health, no shield and light armour for extra mobility. The key to this fight is gaining maximum damage, I used the Peacekeeper heavy attack to inflict as much damage as possible before reaching the phase transition. Only carry out the heavy attack and invoke Shift when he pounds the ground, he killed me almost every other time. The timing and distance for the attacks is important. Attack too early and too close and the ground pound will kill you, If you are too late and too far you will miss and he turn and kill you. When I was close to the transition I invoked Shift and the heavy attack of the Peacekeeper and the massive one hit almost kills him. This left a slither of health that I took down with the Between.
If you don't inflict enough damage before the Judge jumps to the balcony and then when he jumps down and regains his health from the mob. He will recover his health back to the starting value, and you will be back to the beginning. Now he attacks by sending missiles through the ground which lower your Vitality if they connect, making the fight even more difficult. Be aware the achievement did not pop for me when I used Shift on the Between for the final kill (Thanks TriRock). I used the Trinket Amulet of the Betrayer to increase the damage of the critical attacks.
Another tip is to use Power saving mode to reset the game fully, as I believe the game state is stored in memory between kills and can reduce the HP of your weapons.
The build:
Lvl 229
Weapon: Peacemaker Damage 605, Flawless Luck Rune
Weapon: Between Damage 190, Flawless Poison Rune
Shift 3/3
Str 52
Vit 11
Faith 26
End 33
Ag 8
Luck 0
Weight 8.5/75.00
Health 142
Endurance 288
Magic 156
Amulet of the Betrayer
This tip was found by @Kanchanaburi 19 Nov 2017
Important note: Do not attach the rune to your Keeper weapon as the achievement did not unlock for me after defeating the end boss. However, I was able to use an offline save on my other console and right before the fight, where I used the rune on my armour and a luck rune on my weapon and it unlocked right after.