Originally posted by Emilia Tempest: Use armor piercing attacks (usually heavy attacks for most weapons).

Blunt weapons (maces, hammers) do usually well against armor. greathammer does it with light attacks, maces and greatmaces do it with heavy attacks
Axe weapons (1h-axe, greataxe, crowbil, elven axe, axe&shield) do well against armor on nearly all attacks, light or heavy.

And all other weapons usually do well against armor with heavy attacks.
However, weapons that do stabs (rapier, spears) usually arent that great against body-armor and rely more on headshots.

And for ranged, handguns (kruber/bardin) work well against armor.
Repeater handgun (kruber) works well against armored rats (doesnt work well on cata, but anything below it).
Bolt-staff on sienna can do good damage (use "Volcanic Force" on Battle Wizard to get a feel for the fully charged bolt).
Fireball-staff left-click spam can do good damage against armored rats.
Crossbow (Saltzpyre and bardin) works well against armored rats (needs 2 bodyshots on legend, should work with 1 shot on champion and below).
Brace of Pistols (Saltzpyre) works well against armored rats.
Longbow (Kruber Huntsman only) works well against armored rats, with ult works well against chaos warriors too. (headshot = oneshot on legend and below)
Longbow (Kerillian) works well against armor but only on headshots.
Swiftbow (Kerillian) works well against armored rats, takes about 2-3 arrows (charged shots not hip-fire)

For hitting the head of a chaos warrior, you have to aim left + further above his head. His shoulderplate on the right DOES eat up hits, so attacks to his right side of his head more often than not hit the shoulderplate first.

For melee headshots in general its better to aim a bit above their head than actually for their head. Do keep in mind the angle of your attack, strikes from above are more likely to hit the head than strikes from below. And your attack will count whatever it hit first, if the enemy raises their arms and you do an horizontal strike to their head, youre more often than not hit their arm, despite aiming for their head.
This is a very good breakdown. The part about the Chaos Warrior hitbox seems extra relevant for this post, as OP mentioned bonking dudes in the head and still getting the 'armored' warning - that should not happen on any headshot.