I don't think the Giant Bomb achievements system is too active (in fact, it's getting phased out), but if you really wanted to refresh it right away you can go to your profile's achievements page, Click "Manage Your Accounts" and you should see a list of your accounts and a refresh button. Click the refresh button and wait a bit and it should update.
im not seeing a refresh button:
No one will ever see them.
I dont care about people seeing them. Im more interested in comparing my acheivements to other peoples, and seeing which of mine are rare or uncommon achievements.