PAC-MAN MUSEUM

There is a spot on level 1 of Pac-Man where you can hide and the ghosts will never go. Just hide in that corner while using a wired controller and leave your console on.

To be on the safe side, clean up the dots near the hiding spot, enter it from the left (not from below), and don't let any ghosts see you enter it (or they'll go into pursuit mode and nab you). If you do this over multiple sessions, I'd advise finishing the game and then backing out to the main menu to ensure your time is recorded.

The achievement pops when you finish the game.

Here's a video (not mine) showing the location.