Here is the full list of all 13 Quake II achievements. It takes around 20-25 hours to unlock all of the achievements on Windows.
Call of the Machine: Collect all six Data Discs, and defeat the Strogg Creator
Ground Zero: Find and eliminate the Strogg's great weapon, the Gravity Well
The Reckoning: Infiltrate the Strogg Moon Base, and destroy the fleet
Quake II 64: Enter an alternate timeline, and destroy the Guardians
Quake II: Neutralize Strogg leader's communication system
Quake II: Close main hangar bay door and destroy the Black Hole Generator
Quake II: Find and destroy the Strogg's planetary defense system, the Big Gun
Quake II: Infiltrate and destroy Strogg main reactor
Quake II: Shut down all machines in the Strogg processing plant
Quake II: Navigate the mines to find a service entrance to the factory
Quake II: Enter the security pyramid and destroy the security grid protecting the industrial region
Quake II: Destroy the Strogg logistical train and restore power to key warehouse components
Quake II: Establish a communication link to the command ship