Avoid getting caught in Under Pressure. Stay underground on blue floors and only pop out on yellow floors. You must also avoid mines, the ledges, and other obstacles that'll force you to stop burrowing along the way, cause if CH1P catches you popping out before reaching the yellow floor, you'll have to back out and try again. Achievement/trophy pops if successful, same solution goes for the Pixel Rider achievement in the last game as well.
EDIT: Some gamers confirmed that if you accidently get caught by CH1P, you can kill yourself and try again. IDK how was it possible, but I personally didn't do this method.