Here is the full list of all 35 QUAKE achievements. It takes around 20-25 hours to unlock all of the achievements on Windows.
Kill a monster with another monster's attack.
Find a secret area.
Complete Quake Episode 1: Dimension of the Doomed in single player.
Complete Quake Episode 2: The Realm of Black Magic in single player.
Complete Quake Episode 3: The Netherworld in single player.
Complete Quake Episode 4: The Elder World in single player.
Defeat Shub-Niggurath in single player.
Complete Scourge of Armagon Episode 1: Fortress of the Dead in single player.
Complete Scourge of Armagon Episode 2: Dominion of Darkness in single player.
Complete Scourge of Armagon Episode 3: The Rift in single player.
Complete Dissolution of Eternity Episode 1: Hell's Fortress in single player.
Complete Dissolution of Eternity Episode 2: The Corridors of Time in single player.
Complete Dimension of the Past in single player.
Complete Dimension of the Machine in single player.
Find the secret exit in Quake Episode 1: Dimension of the Doomed.
Find the secret exit in Quake Episode 2: The Realm of Black Magic.
Find the secret exit in Quake Episode 3: The Netherworld.
Find the secret exit in Quake Episode 4: The Elder World.
Find the secret exit in Scourge of Armagon Episode 1: Fortress of the Dead.
Find the secret exit in Scourge of Armagon Episode 2: Dominion of Darkness.
Find the secret exit in Scourge of Armagon Episode 3: The Rift.
Find the secret exit in Dimension of the Past.
Find the secret exit in Dimension of the Machine.
Find the Well of Wishes in the Crypt of Decay.
Find the secret message in Tur Torment.
In deathmatch, electrocute an enemy in water without dying.
Kill a shambler before it is able to cast its lightning attack.
Kill a shambler with an axe.
Complete E4M6: The Pain Maze on Nightmare without taking damage.
Complete E1M1: The Slipgate Complex on Nightmare without firing a shot.
Complete Quake on Nightmare in single player.
Complete Scourge of Armagon on Nightmare in single player.
Complete Dissolution of Eternity on Nightmare in single player.
Complete Dimension of the Past on Nightmare in single player.
Complete Dimension of the Machine on Nightmare in single player.