There are three main ways to inflict damage in Perfect Dark, shooting, melee and explosives.
Perfect Dark uses a location-based damage system, where different body parts take different amounts of damage. In general, assuming a shot to the body gives 1x the "normal" damage, a shot to the leg or arm will give 0.5x the damage, and in Combat Simulator, headshots do 2x the damage.
In campaign, the Skedar also take double damage from a headshot. Versus humans, headshots work differently. In fact, a single headshot will kill any unshielded AI character using any gun, on any difficulty. Even when health has been modified to 1000% in Perfect Dark mode, this holds true.
Crossbow: On sedate mode, the crossbow will KO any unshielded human enemy with 1 hit to any part of the body. This mode does zero to negligible damage versus Skedar. This is true for any difficulty, and modified health values.
Tranquilizer: The tranquilizer's main mode will KO any human enemy with 3 hits to any part of the body, including the head. This mode does zero to negligible damage versus Skedar. Again, this is true for any difficulty, and modified health values.
Combat Knife: As far as the damage mechanics are concerned, a hit with a thrown knife acts just as a bullet, except it poisons them, causing damage over time for a while. This poison damage continues after respawn in Combat Simulator.
FarSight XR-20: The Farsight will kill any unshielded enemy of any race with any health modifiers in any game mode in one shot, making it one of the most powerful weapons in the game.
Laser: The short range burst will not kill an unshielded enemy with a single headshot, if their health has been increased in Perfect Dark mode. It's probable that headshots give a large damage multiplier, but since the beam's damage is so low, it is still not enough to kill.
Psychosis Gun: The Psychosis Gun does no damage, although an enemy shot in the leg or arm will move like they took damage in that region.
DY357-LX: The LX will kill any unshielded enemy (including Skedar) in one shot, no matter where it hits, like the Farsight.
Melee attacks appear to have three hitzones, the upper third, middle third, and lower third of the entire body. The upper third does 2x the damage, middle does 1x and bottom does 0.5x. In Combat Simulator, an attack from behind causes double the damage.
In campaign, the Skedar also take double damage from behind. Versus humans, a single hit from behind will KO/kill any unshielded AI character on any difficulty, even when health has been modified to 1000% in Perfect Dark mode, provided they have not spotted the player.
Combat Knife: A knife slash from behind will kill any unshielded player in one hit in Combat Simulator.
Reaper: The Grinder function will not kill an enemy from behind in one hit.
Explosives cause damage over time in an area, with damage being strongest at the center and decreasing with distance, meaning the total damage is highly variable.
It appears that unshielded human AI characters in campaign die instantly if in range of any explosion, regardless of difficulty and health modifications.