Don't sprint everywhere - you'll just ram into walls all the time, which is useful for stunning enemies, but annoying when you actually want to get anywhere.
Secrets
Make sure to return to levels with new cats to unlock new routes - there's a bunch of secrets to uncover all over the game.
Time penalty
If you don't mind the time penalty, taking a hit against an enemy can prove handy for progress, as most of them die after you touch them.