At the risk of ruining my recent success over the last 64 games with her, I'll post what I posted on the Diddy Kong page:
As someone who recently moved from Diddy Kong to Rosalina as a main, I find it hardest to deal with play-styles that put immense pressure on me. Rosalina has a fair amount of ending lag to most of her moves. They have good range, knockback, and quick start ups - but if I'm not careful I get punished hard. Your typical Little Macs, Captain Falcons, Yoshis, and Shieks all piss me off with their ability to rush me down. I can typically evade the first one or two obvious attacks, but what makes them excellent rushdown characters is that they have little to no ending lag - which means I find it very hard to punish them after missing they miss once or twice.
The characters and play-styles Rosalina does best against are your typical campy guys. In my experience I've found that I can usually out mind-game everyone that tries to play like this. She has so many tools at her disposal to both approach campers, punish would-be campers, and force habitual campers to approach.
So in sum, my advice: Rush down Rosalina. Don't stop the pressure. As soon as you've got Rosalina and Luma separated and you're hitting Rosalina - you have the advantage. If she recovers and gets Luma by her side again, side B through any walls she puts up and keep pressuring.