To unlock the Born in Battle trophy in Anthem, you will need to complete three of the Marksman Rifle challenges which can be found by opening the Menu > Challenges > Weapons > Marksman Rifle
You will find four challenges available -- one for each of the game's three Marksman Rifles, and a final one for completing all three of the Marksman Rifle challenges.
The three challenges you will need to complete are 50 kills with the following three weapons:
Scout
Guardian
Anvil