This is the most annoying achievement in the game, but there's an easy way to get it - you'd only need to dodge once to get it using this method.
Load up the first level (Shipwreck Reef) on chapter select, and use Spongebob. Play until you reach the skydive section, and jump in. Once it begins, move all the way up, until you pass a steering wheel on the top right (this happens just a few seconds into the dive). Immediately steer all the way right, and hold your controller and character at the top right of the screen.
As long as you're constantly holding the top right position, nothing would hit you as you dive through the hole... until right at the end. There will be one piece of plank right before you reach the end of the tunnel, and this is when you need to dodge slightly left, until your character is at the top centre of the screen. Beware not to steer too much left, as there's also a plank on the left.
It may be beneficial to leave yourself with one yellow bar of health before attempting this, i.e., half a bar left. This is because if you do happen to hit something, and die, you'll begin right at the start of the skydive. The downside is, if you do fail, there's no way to reload the checkpoint to try again. Instead, you'd have to use chapter select, and watch through the unskippable cut-scene again.
PS: Just to clarify, I mentioned to use Spongebob, because he's the shortest of all the characters. I tried the same method with Squidward and Sandy, but they were hit by a small piece of plank halfway through. It appears that only Spongebob could squeeze past this piece by just holding the top right position.