This trophy's description is a bit misleading. You don't need to score 256 points in your current playthrough but instead you need to earn a streak of 256 points or dots consumed at some point while playing.
You earn a single point per dot consumed, and you'll notice the current score streak underneath Pac-Man as he continues to eat the dots. The value will increase so long as you choose a path that does not have a break in the line of dots. Once you reach 256, you'll unlock the trophy and clear the screen of ghosts.
You're better off trying to get this done right from the beginning of the current run. The best way to approach this is simply by looking ahead. Glance ahead and make sure you can find a path where the dots flow uninterrupted. Work your way up the maze by moving along the horizontal plane more than vertically, since as you progress vertically there will be more ghosts ready to trap you. Always try to plan a path that moves you toward a power pellet, so that you can eat the ghosts and give yourself more path options.