Defeating the game’s bosses is difficult with even the best weapons, so you should do a few playthroughs to learn the nuances of each fight before attempting the challenge.
To avoid an accidental mixup or stop Leon from using the game's best pistol, only stock handguns and knives in the inventory. Magnums aren't classed as handguns, so avoid those.
Ensure that Leon is using the best handgun and an upgraded primal knife. Get the primal fully leveled up, and Leon won't need to worry about it breaking during combat.