Does she have any? At all? Thanks to Luma, you can't approach her, you can't grab her, and you CAN'T EVEN PUNISH A SHIELD BREAK (Just got knocked out of a tournament because of that. The salt is absolutely real.) Her own frame data is pretty decent, so staling all of your moves for 8 seconds of no Luma isn't a good option. Are there any cracks in this stone wall?
EDIT: You can't combo her either, since Luma can move around freely regardless of whether Rosa is in hitstun or not. Seriously, shield break? ****ing really, Sakurai?
Rosalina's fastest move is dtilt, at 5 frames. Luma's fastest grounded move is utilt, at 3 frames, although I've literally never seen anyone use utilt as a GTFO option. Getting past the Great Wall of Luma is admittedly tricky, but if you do, Rosalina lacks fast CQC options.
Here's what Luma can do to free Rosalina from sticky situations, and the mechanics behind it:
Grabs: Luma can free Rosalina from a grab. First, Rosalina can simply input a fairly quick attack such as jab before getting grabbed, but not fast enough for her hitbox to actually protect her. In such a case, she'll be grabbed but Luma, who cannot be grabbed, will still proceed with its own version of the attack. This will hit the opponent and free Rosalina.. (It's important to clarify here and now that Luma will never, I repeat,
NEVER, attack of its own volition. Whenever it does anything other than move around, it's because Rosalina pressed a button.) In rare and not-completely-understood cases, Rosalina can also mash buttons while being pummeled and make Luma attack, although I'm personally uncertain as to what limits exist on this ability. The correct action to avoid getting bopped by Luma is to throw Rosalina immediately without pummeling, and do not try to beat her faster options with a grab. (If Luma is absent, you can of course pummel all you like.)
Combos/Strings/Followups: If an attack hits Rosalina but not Luma, or if an attack hits both but is not strong enough to send Luma flying, you'll find yourself somewhere nearby Luma while Rosalina is in hitstun. Here it's important to note that you can airdodge out of hitstun before you can jump or attack. Once Rosalina is able to airdodge, even if she herself cannot attack, her button presses will reach Luma and make it attack. When this happens, Luma will start to fly back to Rosalina at the same moment it starts attacking -- imagine a straight line from Luma to Rosalina to figure out how it will move. (This applies only if Luma is linked to Rosalina at the time, i.e. Rosalina did not use Luma Shot.) The correct action here is to either shield Luma's attack, hit Luma quickly with a reasonably fast move (Luma cannot do anything when it's in hitstun or in a tumble animation), or avoid the line from Luma to Rosalina when moving for your followup. Since the time to Luma's counterattack depends on Rosalina's hitstun, you will have more time to do whatever when Rosalina has more damage.
Sleep/Stun: When Rosalina is asleep or stunned, she can still press buttons to make Luma attack. When in the air from a shield break animation, she can make Luma do any aerial except bair, and when asleep/stunned on the ground she can make Luma jab (including the gentleman and rapid finisher) or do a tilt, but she can't make it do a smash. The correct action here is to swat Luma away with anything strong enough to send it flying before moving in on Rosalina. Alternately, use something that outranges Luma, but be aware that Luma's second and third jab will move it forward, so Rosalina can give it a little extra range that way.
Helpless: When Rosalina is in helpless fall state after using Launch Star, she can make Luma perform any aerial except bair. The correct action is to simply be aware of this and time/space your punish to avoid Luma -- from behind is best given the restriction on bair.
Landing: When Rosalina lands on the ground, she can perform an aerial a few frames before landing. Done correctly, she will land without any landing lag since the attack has not even started yet, but Luma will still perform its version. Since she incurs no landing lag, Rosalina is free to act while Luma attacks. If Luma is linked to Rosalina at the time, it will follow her as she moves around. This technique is known as Lunar Landing. The correct action is to be aware of this option and be ready to punish improperly timed attempts -- the techinque requires single-digit frame precision (exact numbers depend on the aerial she uses) and performing it too early will result in normal landing lag. Performing it too late will result in a normal landing followed by a jab, tilt, or smash depending on what buttons Rosalina pressed.
Land Mine: When landing on the ground from hitstun or helpless, or when recovering from sleep or stun, Rosalina can mash the jab button to make Luma perform its rapid jab, then hold the button before she herself does her own rapid jab. She is then able to move around freely while Luma continues spinning in place, wherever it is. She can even perform tilts, smashes, and aerials by very briefly releasing the button and pressing it again -- if she's fast enough, it won't interrupt Luma. She cannot use specials without making Luma perform its finisher. The correct action here is to hit Luma with literally anything -- hitstun will break it out of its rapid jab.