To get this achievement, you must complete any level with a time no slower than 3 hundredths of a second slower than your next star rating.
While it may seem like 0.03 seconds is an EXTREMELY small window to need to miss a star rating by...In reality, the requirements to achieve a 3 star rating are so finely tuned that you will very likely get this just by attempting to 3 star every level for the "Woooooooooah - livin' on a prayer" achievement.
The only real advice I can give is to make sure you actually COMPLETE each attempt at a 3 star even if it isn't exactly perfect. While this may seem obvious, the more I played the game I developed a tendency to hold RB for the tiniest mistakes which led to me only actually completing a level on a 3 star run.
If you're struggling with a particular level, as long as you have a hint token available (acquired by winning crate smash, a game ran by Kat in the Greatbeard Arcade located on the dock) you can use a hint to have a ghost show you an optimal route.
For informational purposes, I acquired this achievement in 1-4 while playing through the campaign.