Predator's Path quests can be unlocked after liberating garrisons. There are 13 garrisons spread out across the map. When looking at the big map, unliberated garrisons look like hexagons with a red center, while liberated garrisons have a green center.
There are 8 Predator's Path quests spread out among the 13 garrisons. After liberating them, a mission machine will be active inside the garrison in which you must accept the mission. Sometimes the missions will require you to use a certain weapon to obtain the kill. Failure to kill the animal(s) with that particular weapon will fail the mission and the mission will restart without penalty. If a particular weapon is needed, the game will always send you to a place on the map for that weapon type and several ammo refills.
I will keep the particulars of the missions spoiler free as some of them are pretty cool/funny and pay tribute to the 80's. Weapon attachment unlocks occur after certain PP quests are completed.