To unlock the Archery Expert trophy in Far Cry New Dawn, you will first want to craft the Lucky Shot Compound Bow -- you will need to upgrade the Workbench at Prosperity to level three in order to craft it.
Once you have crafted the Lucky Shot Compound Bow, it has a sight that will allow you to aim for over 100m and account for arrow drop.
To any outpost or location where there are lots of enemies that are preferably stood still (the video below uses Bullet Farm), set a waypoint so that you can gauge when you are 100m away, use the sight to set the distance and fire a basic arrow to kill them.