If you don't care about the score achievements and want to get this achievement out of the way, simply stay away from the sleeping ghosts and do not eat anything.
At the one minute mark, a red ghost (Blinky) will appear and attempt to chase you. However, if you go from one end of the tunnel to the other, it won't be able to catch you. Blinky will only use the tunnel if it sees you, so if you move to the other side of the maze in time you'll have no problem avoiding your pursuer. At that point it's just a matter of letting the timer run out.
I did eat a few pellets during the last seconds to score some points, but I don't think that was necessary.