You must complete all of Course 4 (all 9 chambers) without you or your partner ever dying. You must start from Chamber 1. If you or your partner die, you must restart from Chamber 1. The achievement will pop soon after you insert the disc into the player.
In my opinion, the last two chambers are really the only ones that may give you issues without preparation. Chamber 8 has the "spike maze," be sure the one inside is quick with the portal gun and the one outside is quick with the button. In Chamber 9, be sure the person controlling the light bridge covers all your tracks so a stray turret doesn't kill you. I recommend playing through these last two chambers until you and your partner are comfortable with the puzzles before starting this achievement.
If you have everything fairly memorized, the entire course should only take about 20 or 30 minutes to complete.