You obtain the advanced portal gun in chamber eleven. For the remaining levels, you have to make sure that you only step through the orange portal. Be especially careful not to sit in the middle of a portal because the game may consider that to be passing through the blue portal. Just move through the portal as quickly as you can. Save frequently, so you can reload if you accidentally step through the blue one. The achievement will actually unlock right after you destroy the last piece of GLaDOS to beat the game.