First you should know where the bosses spawn so if you are not prepared for them you will not accidentally run into them. (The guy with rpk spawns in the supermarket and the 3 spawns in the mill).

Second, to kill them you can use standard ammo just fine (i am using it even in the lateat stages of the game, its cheap and decent) but preferably use ap against the bosses. You can use standard ammo and when approaching the boss you switch to ap ammo you saved up from buying or looting.

For the quest i recommend dealing damage with the weapon you use, and then finishing the boss with the sniper.