There is a Final Boss in every Public Dungeon, once you kill this boss you get a Skill Point. I believe each Final Boss in Public Dungeons have an achievement associated with them, if you are concerned about keeping track of them.
The two achievements I have arrows to are prime examples of achievements that track the defeat of Final bosses in Public Dungeons.
I have broken them down to the easiest most comprehensive form possible. Zone, Name of dungeon, person/persons you have to kill or event you have to complete for skillpoint.
-Stonefalls, Crow's Wood --
Destroy the South Wraiths to summon Ghyslain and then slay him.
-Deshaan, Forgotten Crypts -- Eradicate the Kwama infestation and kill the Kwama Guardians.
-Shadowfen, Sanguine's Demesne -- Kill fight-Master Grel and his adepts.
-Eastmarch, Hall Of The Dead -- Defeat Reynir the Destroyer and his minions.
-The Rift, Lion's Den -- Kill the Lonely Giant and his angry Mammoths.
-Glenumbra, Bad Man's Hallow -- Slay the Giant Snake Mother
-Stormhaven, Bonesnap Ruins --
Slay the Eternal One
-Rivenspire, Obsidian Scar --
Slay Zilbash the Deciever.
-Alik'r Desert, Lost City of the Na-Totambu -- Solve the Puzzle of the Guardians.
-Bangkorai, Razak's Wheel -- Defeat the Flesh Atronach.
-Auridon, Toothmaul Gully -- Destroy Bloodroot and its guardians.
-Grahtwood, Root Sunder Ruins -- Complete the Root Sunder Ruins Group Event
-Greenshade, Rulanyil's Fall -- Defeat the undead hordes of Hergor the Fallen.
-Malabal Tor, Crimson Cove -- Kill Flat Tooth and his boys
-Reaper's March, The Vile Manse -- Defeat the damned creations of Graccus' frost experiments.
Village of the Lost -- Defeat Zatalguch in its subterranean lair.
16 in total.