Rayman Pirate-Community

Especially at the beginning of the game. What's the trick? I assume it has to do with racking up a lot of points because I don't think I'm missing collectibles.

Racking up points is indeed difficult – in fact, we have a 388-page topic on it!

The most basic tips I can give you are to try to build up your combos as much as possible, make sure you're not missing any secret rooms*, and try to score points while equipped with a superpower (detergent can) so that they are doubled.
* Not sure if we've a list of them anywhere on this site and if not we really should. You can search for them online anyway.

Getting the secret rooms and the "natural" combos is often enough for 100%, and if not, then at least 80%.

To get the smiling Murfy for every level it is not typically required to get 100% in every segment.

IMO, aiming for a high score during your first playthrough is counter-productive. You will spend tons of time repeating and retrying sections and will get frustrated. Beat the game first, become skilled at it, then work on improving your score.

Rayman 3 is a fairly easy game when it comes to general play, but scoring is by far the toughest element in the game. Obtaining 100% in each part isn't a walk in the park when you're new to the game, it would require some combos that might take time to get the hang of at first. As said above though, just be sure to find secret rooms.

Also, try have a combat fatigue as often as possible while collecting gems or defeating hoodlums, this yields double points. Whenever you see a green gem, try be sure to at least collect other gems or defeat enemies before collecting it, since the combos start to multiply after 5 items, and green gems are worth a lot.