As well as unlocking the "Under a Buck" Achievement/Trophy, shooting the deer trophy in the Admiral's Quarters in "Chapter 4: History's Ember" also yields a small amount of Tungsten – most likely the first Tungsten the player will get.
There may be a reason why this particular resource is so rare. It has been stated throughout the franchise that humanity is running incredibly low on resources, prompting Planet Cracking. As a natural resource, tungsten would be very hard to mass-produce, in contrast to a resource like Somatic Gel, which can be mass-produced to yield a large amount.
Tungsten is a strong, lightweight metal with high temperature and electrical resistance.