I saw that in the few runs doing this category, at the start of the level there is a regular crystal that "requires" you to fall with the cart as you collect it.

Instead, you can collect that crystal by holding right in addition to holding left - Croc will tilt very slightly to the right, and will manage to collect that crystal, without falling.

Will only save like 5-10 seconds though, but could be nice.

Just tried it and it works. Thanks for letting us know