To unlock the Old Reliable trophy in Days Gone, you will need to kill 200 enemies with a crafted weapon.
The only weapons you can craft in Days Gone are melee weapons and throwables. You unlock new crafting recipes whenever you complete an Ambush camp. During the story, you will automatically receive the recipe for the Spiked Bat, which will require a bat, nails and scrap to craft.
Melee weapons will only last so long before the break. A good strategy is to get the Field Repairs Melee Skill so that you can repair your weapon with scrap rather than letting it break.