First thing, make sure you are not on "Easy" difficulty.
Then you can start the game, best is the first chapter of the first story.
Find the fastest path, and just dash and jump through the chapter.
Careful not to accidentally bump or stomp any enemies.
Once you reach the end, then you should be able to get this achievement and also a DOUBLE achievement if you havent completed the previous one that doesnt require not taking damage, and make it a TRIPLE achievement if you do it under 30 seconds! ;)