Load up the Act IV chapter Nightmare Riders. Here you’re going to want to move around the walls as close as possible without hitting them. If done correctly you will see a yellow circle in the center of your screen with 2,500pts. The multiplier will increase for every wall you pass by without hitting. You need to move around the wall at the very last second without clipping it.
Hitting walls will temporarily make your character flash and won’t allow you to obtain any additional near-misses until your character has stopped flashing.
Just keep reloading the chapter until the achievement pops. This took me less than 5 mins to do once I had completed the game.
P.S. Thanks to ZombieExy for confirming that you can unlock the achievement while using the dodge buttons.