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In Team Fortress 2 (another Valve-created Source Engine game), there's a menu in-game to display the achievements one has earned. There is also a function to display specific achievements on the HUD.
Is this in Counter-Strike: GO?
Unfortunately, no. The only way the player is notified of achievement progress is via those little messages that appear on his or her screen when he or she actually unlocks one.
Required, but never shown