Robin is a good character but he gets bodied by rushdowns so hard (most notably Fox, thanks to blaster spam and the reflector). Rosalina is not that, and is in fact one of the two top tiers that is not a rushdown or hybrid. Unlike Yoshi, she doesn't have a projectile either, so that's a problem in this matchup.
I have surprising difficulty getting in on Robin thanks to all of his projectiles. Yeah, I can GP them all, sure, but that isn't exactly safe at melee range. When we're close enough to be considered melee range (which to be fair is still quite far for Rosalina), GPing a grounded Robin's arcfires has to be a read, because it can't be done on reaction (lasts too long) and it can't be shielded since it goes off regardless of what happens unlike Ness' PK Fire. It also takes out Luma if it's shielded.
Let's talk about aerials. Bair and Uair are nasty and I'd never touch those with a 30 foot pole at 80%+. Fair is slightly slower IIRC but it's still scary. A good Robin probably also has next to no difficulty spiking our recovery with his Dair from far away, a location that's not uncommon for us to be since Robin can blast us so far. Robin hits hard and fast and in every direction because of his nice set of aerials (I'd recon he would be top tier if not for his ****ty running speed). And we're a very large target, so he doesn't have much trouble punishing bad spacing.
Rosalina can get away with aerial hit and runs with nair, but our grounded options are risky since his arcfire outranges them. Ironic, considering it's normally the other around.
Robin has all the tools to space against us and all of the tools to kill us. This is probably his best top tier matchup.
Of course, Robin having all of these keepaway defenses does nothing to help him kill Rosalina, just keep her out. Rosalina's advantages I'm sure either have or will be touched on, so I won't comment to much on them. But uh...
+0 without customs
With customs, this obviously becomes significantly worse for Robin for the same reason as every other projectile spacer fighting Rosalina. SSL just annihilates him. She gets the projectile she so desperately wanted and Robin feels that in full force.
+2 with customs