GP are useful against his projectiles as long as you don't get baited for him to punish your end lag. Because of Rob using gyro for edgeguarding because he can use it near the ledge to limit your ledge options(get up and jump, think) for him to either read your roll or you getting off the ledge to attack for spacing. Rob can live longer than Rosalina since he's heavier than her and she's light so be careful of his rage since his attacks can even kill her early. Watch out for the up-throw because he can even get early kills from platforms along with rage. If you know your combos besides out of down-throw and up-throw, then Rob is a easy target for them and getting by your up-airs. If you jab 3-hit finish, then you may get a free combo with your up-air, depending on his di and if you read the air dodge, then free punish. Plus, read the air dodge for a up-air if you can because unless he has a gyro and he can drop it under you, then he can't challenge your dangerous up-airs any of his aerials. Be careful of his zoning because of his aerials, gyro, and lasers. Jumping over the lasers and gyro may help along with Power-shielding(but Luma will get hit). Up-tile and up-smash as anti-air moves when needed. Don't challenge his up-smash while landing if you get jiggled. Plus, watch out for the gyro because he also mindgame and bait your landing with them for him to punish. I think her b-air(or SH) can deal with his n-air along with her forward-smash(but spaced, though), and maybe star-bits. To deal with gyro, dash attack, SH aerial, SH air dodge to catch the gyro, but time it right so you won't get landing lag or try to less. Edge-guarding, B-air and down-air(along with Luma's hitbox) are your to go for gimping. Also, if you have the gyro in your hands, mix up it by z-drop to bait an air-dodge for a gimp or pressure him off-stage with it by limiting his ledge options. Down-smash for a ledge punish(or kill), down-tile, down-air(halo hitbox) to spike Rob down, and angled forward smash for ledgeguarding. Also, place Luma near the ledge for you to limit his ledge options for pressure and if he rolls, then down-smash to-go hit. Plus, if he tries jump away off-stage from the ledge, there's a few things you'll see. One, jumping to attack you so if you see it, punish him however you can. Two, if he grabs the ledge again, then free ledge punish or kill with Down-smash or aerial(back-air for a stage spike). If he tries to recover high(and go for the platform), then use your up-air or up-smash if he tries n-air. Plus, bait out an attack from him or a air dodge if you can for a punish. If he tries to recover medium, then forward smash, jab, baiting, reading his landing, or mindgame.
Stages: Lylat Cruise, avoid it because he does well with in it, thanks to his size, range, and projectiles and the moving stage can screw over your recovery. Duck Hunt is ok because both can live longer(Rob mostly), and can't stage spike each other. Battlefield, Rob can use the platforms for his projectiles to bait, combo, and trap, and also can early kills with up-throw; Plus, SH aerials as well under the platforms and jiggle her under them. Rosalina can SH aerials under the platforms for mindgame, zoning, and pressure. Also, thanks to her height and range, she can up-tile and up-smash under the platforms and jiggle Rob more and give him trouble, landing so this stage is good for both of them. Delfino Plaza, while Rob can get early vertical kills with up-throw and up-air, Rosalina can do the same as well with up-smash, up-air, up-tile, and up-throw, thanks to the low ceiling so this stage may help her more because of Rob's weight for her up-air to combo and even get early kills with Luma. Same with Halberb. Dreamland, ok for both of them since its similar to Battlefield, but with alittle more space, the wind blowing, and the ceiling being alittle lower.
Customs: I got nothing on Rob's and only on Rosalina's.
Results: This MU favors Rosalina by +1 in Default only; No customs.
can live longer, edgeguard, jiggle, and use his projectiles on Luma(even if Rosalina power-shield).
can jiggle better because of Rob's weight and unsafe landings(outside of gyro), deal with his projectiles with GP so camping won't work much, get through his zoning with Luma, combo him, and also gimp him as well. So, she can get through his options with zoning of her own, use GP, and he's combo-meat for her if you know her strings and combos so get out there and take him down.