Underworl damage types.

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Chaos, dark and light damage won't ignore protective spirit anyway. It seems that only vampiric touch skill goes through it and do full damage. One touch can kill 55 hp monk. If there is enemies in UW which use that skill, you can notice it when caster comes next to you. There is not tricks how to avoid them. Just watch what skills they use. Only necromancers have vampiric touch.

Aside from attacks, only skills that say "damage" in the description do damage. Stealing life is not damage. Order of the vampire, vampyric gaze, barbed signet, etc. will ignore prot spirit.
There is currently no way to push damage through prot spirit.

Off the top of my head:

Banished Dream Riders - Chaos damage - easily avoidable if you don't like the Chaos planes

Dying Nightmares - Dark damage I believe, looks like it to me

Vengeful spirits - Chaos damage from Illusionary Weaponry - only accessible through the Vale quest

Keeper of Souls - Dark damage I believe - only accessible through the Unwanted Guests quest

No idea what the Terrorwebs' regular attacks are, don't recall them being elemental (didn't trigger Essence Bond when it was physical only though so that counts physical out).

Just some fixes and additions to above:

Vengeful Spirits : Physical damage melee, and just plain damage* with IW. Its not chaos.

Terrorwebs : Dark damage, with continuous fire spell attacks.

Dead Threshers : Not sure, but I would bet on dark damage.