I actually filed a bug report of this, and it's apparently "working as intended".
It's another one of those stupid "do the fight our way or we will wipe you" mechanics, like in Ifrit Extreme. Put simply, your DPS were too good for the fight and pushed his phase. Which results in Leviathan going "lolno" and killing you no matter what.
My advice is to stop damaging Leviathan as soon as Mercy Stroke and Misery's End pop up, as he seems to hit his "NOPE" button around 17%.

As I put in my bug report, my group was able to do this in i90 with i95 weapons. This fight is going to be nigh impossible to do with this mechanic when people are going to be sat in i110+ Pulling away the finishing line as you reach it is not a good mechanic.