WoWDB

To get these achievement, you need to clear mythic https://www.wowdb.com/zones/8440-trial-of-valor without dying a single time. 

What happens is that at the start of the instance, you will get the buff https://www.wowdb.com/spells/232301-test-of-the-chosen.  If you die at any point in the instance, you will lose the buff and fail the achievement.  If you have the buff on you still when Helya dies, you will get the achievement and title.  This is an individual achievement, so your raidmates can die as much as they want.

As a note, you must be in the instance for the first boss in order to get the buff.  You cannot cheese it by waiting until the last boss before zoning in.  You will either get the buff when you initially zone in, or the first boss will apply it to you at pull.  If you miss either of those, you won't get the buff.

This achievement stands a good chance of being removed by Legion's conclusion.  From @WarcraftDevs (source): ""The Chosen" will likely go away eventually, possibly when the Legion expansion ends, but we don't plan to end it in the very near future."