To level up the Sniper Rifles skill, you need to shoot enemies with bolt-action rifles and reload. These rifles include: All types of Mosin Rifles, SV-98, DVL-10 “Saboteur,” Remington M700;

Taking the Mosin Rifle and several packs of LPS ammo is recommended. Go kill the scavs, shooting their arms and legs to receive more points from a single scav, constantly reloading along the way. Beware of the fatigue on the skill progression. You might want to get out of the raid and go into the new one once you reach the level of fatigue that stops your progression drastically.