The Addams Family: Mansion Mayhem

I was able to get this achievement after finishing the story line. I went back and replayed the levels in the music room world skipping the mini-game levels. If you do die and respawn either finish the level and just play it again or quit out from the level and restart. There is no need to exit the whole game or to start the world over.

I recommend taking the shortest routes when possible, don't try and get the crests, and don't worry about collecting doubloons. Skip as many bad guys as possible. All that matters is that you finish the level without having to respawn. I chose the music world simply because the bombs that are the main weapon in the music world give you a bit of a speed boost as well as a kind of shield in that you can accidentally run into a bad guy and it just blows up the bomb giving you a chance to quickly press X and spawn a new bomb before a heart is taken away. This leaves only falling off the sides as a possible way to lose all your hearts, for the most part.

Just for clarity, the levels I replayed and made sure I did not respawn were:
3-1 Musical Madness
3-3 Rootin' Tootin' Terror
3-4 Sinister Strings
3-6 Bell Blast
3-7 Moonlight Sonata
3-9 Symphony of the Fright

As soon as I jumped into the warp field at the end of 3-9, the achievement popped.

This can be done in any four of the worlds. I highly recommend trying to unlock this before the final world as there will be mini bosses, and constant flying to and from platforms that don't always cooperate. Something to keep in mind is that to unlock the final level of the Laboratory world you only need 52 crests. Personally, my best strategy for getting this achievement would be to try to get as many crests as you can in the Dining Room world, and the Graveyard world. The Music world is by far the easiest world to unlock this because the bomb ability basically gives you a one hit shield when you're rolling on it as when enemies attack they get blown up, and you don't take damage. On top of this, once an enemy hits you, while in mid air you can still equip one more bomb before having to touch the ground. Once this bomb explodes you will have to touch the ground in order to use the bomb ability again. Having crests built up by the time you reach the Music world will allow you to just cruise through each level.