The Middle Earth: Shadow of Mordor Height of Despair will give you a Bronze Trophy or 10 GamerScore Points. You need to use Strike From Above while at least 60 feet above your target.
On the map, Just where the game starts, look for the most eastern forge tower of Udûn, this will serve as a very good location to get the Height of Despair
Trophy/Achievement. In this area, you will encounter a few Urks. Hit the R2 + Triangle (PlayStation) / RB + Y (Xbox) to grab the Urk's attention.
Lure him to the upper region of the tower climb up and perform a Stealth Takedown from above (R2 + Square on PlayStation / RB + X on Xbox). To complete this task successfully you must use the Stealth mode, if you are seen, it wont be considered as a stealth kill.
For those who are still unclear about how to get the Middle Earth: Shadow of Mordor Height of Despair Trophy/Achievement, watch the video below: